How To Solve a Quadratic Equation With a Decimal

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Quadratic equations with decimal values are more difficult to solve because the guess-and-check and box methods of factoring quadratic equations are much less intuitively easy for decimal values. Solve these equations by multiplying both sides of the equation by a multiple of ten to eliminate the decimals and using the quadratic formula to find both values of x.

  • Multiply both sides of the quadratic equation by the smallest multiple of ten that will convert each decimal in the equation into a whole number. For example, given the quadratic equation x^2 - 0.2x - 1.2 = 0, multiply both sides of the equation by 10 to eliminate all decimals from the equation, yielding the equation 10x^2 + 2x - 12 = 0.

  • Label the constants of the quadratic equation A, B and C based on the standard form for a quadratic equation: Ax^2 + Bx + C = 0. In the example equation 10x^2 + 2x - 12 = 0, A = 10, B = 2 and C = -12.

  • Plug the values of A, B and C into the quadratic formula: x = (-B +/- Sqrt(B^2 - 4AC)) / 2A. In the above example, plug the values A = 10, B = 2 and C = 12 into the formula to get the equation x = (-2 +/- Sqrt(2^2 - 4(10)(-12))) / 2*10.

  • Solve for first value of x by simplifying the right side of the equation with a positive square root. In the above example, the equation simplifies to x = (-2 + Sqrt(484)) / 20, or x = 1.

  • Solve for the second value of x by simplifying the left side of the equation with a negative square root. In the above example, the equation simplifies to x = (-2 - Sqrt(484)) / 20, or x = -6/5. The two solutions to the quadratic equation are therefore x = 1 and x = -6/5.

References

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