How Do You Solve Quadratic Equations?


Quick Answer

To solve the quadratic equation ax^2 + bx + c - 0, plug the corresponding numbers into the quadratic formula. Take the opposite of b, and provide the option of adding or subtracting the square root of (b^2 - 4ac). Divide the result by 2a.

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Full Answer

  1. Identify the correct constants in the equation

    Consider the example problem 4x^2 + 9x - 2 = 0. Identify a, b and c as 4, 9 and (-2), respectively.

  2. Plug the numbers into the equation

    Render the quadratic equation in the correct format: x = -b plus or minus the square root of (b^2 - 4ac), and divide this result by 2a. For the purposes of this problem, write the equation out in this format: x = -9 + or - [(9)^2 - 4(4)(-2)], all divided by 2(4).

  3. Simplify and solve for x

    Simplify the equation from the end of Step 2. Write the next step as: x = [-9 +/- (81 + 32)]/8. Keep combining terms to yield (-9 +/- (113))/8. Write the two possible solutions as 104/8 or -122/8. Simplify the fractions to yield the two possible solutions of 13 and -61/4. Remember that you should end up with two solutions to a quadratic formula, because the graph of a quadratic formula is a parabola that crosses the x-axis at the x-coordinates that correspond to the two solutions.

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