how to solve quadratic equations?
3711
['Put the equation into the form ax 2 + bx = – c.', 'Make sure that a = 1 (if a ≠ 1, multiply through the equation by. ... ', 'Using the value of b from this new equation, add.']
232042
['You can “manually” solve the equation on the calculator, meaning that if you want to solve the equation ax^2 + bx + c, you basically plug in the quadratic formula into the calculator and hit enter. ... ', 'The second way is faster, but be sure to check that your teacher is okay with you using it.']
969031
Begin by multiplying both sides by the LCD, x(x+1) x ( x + 1 ) . After distributing and dividing out the common factors, a quadratic equation remains. To solve it, rewrite it in standard form, factor, and then set each factor equal to 0. Check to see if these values solve the original equation.
1110156
Use the Quadratic Formula to solve x2 – 4x – 8 = 0 Also, the Formula is stated in terms of the numerical coefficients of the terms of the quadratic expression. Looking at the coefficients in this equation, I see that a = 1, b = –4, and c = –8. I'll plug these numbers into the Formula, and simplify.
199103
['Step 1: Getting Started. You should know that a quadratic equation looks something like this: x^2-3x+2=0 or ax^2+bx+c=0. ... ', 'Step 2: The Equation. Look at the first picture and put that on your calculator. ... ', 'Step 3: Displaying Results. Press program, then the right arrow, then 3. ... ', 'Step 4: Using the Program.']
1192878
['Pick any two pairs of equations from the system.', 'Eliminate the same variable from each pair using the Addition/Subtraction method.', 'Solve the system of the two new equations using the Addition/Subtraction method.']
291177
Another way of solving a quadratic equation is to solve it graphically. The roots of a quadratic equation are the x-intercepts of the graph. Graph the equation. This could either be done by making a table of values as we have done in previous sections or by computer or a graphing calculator.
1466972
['If g = 0, then, again, you can factor the quartic into y times a cubic. The roots of the original equation are then x = -a/4 and the roots of that cubic with a/4 subtracted from each.', 'If f = 0, then the quartic in y is actually a quadratic equation in the variable y2.']
264305
To find the x-intercepts of a quadratic equation, let y = 0. Write down the new equation ax squared + bx + c = 0 and the quadratic formula that gives the solution as x = -b plus or minus the square root of (b squared - 4ac), all divided by 2a. The quadratic formula can give zero, one or two solutions.
325303
['Put the equation in form ax 2 + bx = c. ... ', 'If a ≠ 1, divide the entire equation by a.', 'Add the constant value to both sides of the equation.', 'Write the left side of the equation as a perfect square.', 'Take the square roots of both sides of the equation, remembering to add the “±” symbol on the right side.']
1315032
['Solution.', 'Step 1: Add or subtract the constant term to obtain an equation of the form x2+bx=c. ... ', 'Step 2: Use (b2)2 to determint the value that completes the square. ... ', 'Step 3: Add (b2)2 to both sides of the equation and complete the square.', 'Step 4: Solve by extracting roots.', 'Answer:']
1032178
['Put the equation in form ax 2 + bx = c. ... ', 'If a ≠ 1, divide the entire equation by a.', 'Add the constant value to both sides of the equation.', 'Write the left side of the equation as a perfect square.']
1007046
For a quadratic equation ax2+bx+c = 0, the sum of its roots = –b/a and the product of its roots = c/a. A quadratic equation may be expressed as a product of two binomials.
63463
Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor.
32727
['Step 1 Divide all terms by a (the coefficient of x2).', 'Step 2 Move the number term (c/a) to the right side of the equation.', 'Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.']
245606
Biquadratic equations. A biquadratic equation is a 4-degree equation without the terms of degree 1 and 3. To solve a biquadratic equation you have to do a change of variable: z = x2. Then you have to solve the quadratic equation and finally undo the change.
706683
The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) .