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Simplifying -4.9x2 + 9x = -500 Reorder the terms: 9x + -4.9x2 = -500 Solving 9x + -4.9x2 = -500 Solving for variable 'x'. Reorder the terms: 500 + 9x + -4.9x2 = -500 + 500 Combine like terms: -500 + 500 = 0 500 + 9x + -4.9x2 = 0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -102.0408163 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -1.836734694x + 102.0408163 + x2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -1.836734694x + x2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -1.836734694x + x2 = 0 + 102.0408163 -1.836734694x + x2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -1.836734694x + x2 = 102.0408163 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 102.0408163 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 102.0408163 + 0.8433985840 Combine like terms: 102.0408163 + 0.8433985840 = 102.884214884 0.8433985840 + -1.836734694x + x2 = 102.884214884 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 102.884214884 Calculate the square root of the right side: 10.143185638 Break this problem into two subproblems by setting (x + -0.918367347) equal to 10.143185638 and -10.143185638.Subproblem 1
x + -0.918367347 = 10.143185638 Simplifying x + -0.918367347 = 10.143185638 Reorder the terms: -0.918367347 + x = 10.143185638 Solving -0.918367347 + x = 10.143185638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 10.143185638 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 10.143185638 + 0.918367347 x = 10.143185638 + 0.918367347 Combine like terms: 10.143185638 + 0.918367347 = 11.061552985 x = 11.061552985 Simplifying x = 11.061552985Subproblem 2
x + -0.918367347 = -10.143185638 Simplifying x + -0.918367347 = -10.143185638 Reorder the terms: -0.918367347 + x = -10.143185638 Solving -0.918367347 + x = -10.143185638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -10.143185638 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -10.143185638 + 0.918367347 x = -10.143185638 + 0.918367347 Combine like terms: -10.143185638 + 0.918367347 = -9.224818291 x = -9.224818291 Simplifying x = -9.224818291Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.061552985, -9.224818291}
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