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Simplifying -1x2 + 9x + 120 = 0 Reorder the terms: 120 + 9x + -1x2 = 0 Solving 120 + 9x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + -9x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -9x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -9x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -9x + x2 = 0 + 120 -9x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -9x + x2 = 120 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 120 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 120 + 20.25 Combine like terms: 120 + 20.25 = 140.25 20.25 + -9x + x2 = 140.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + -4.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + -4.5 = 11.842719282 Simplifying x + -4.5 = 11.842719282 Reorder the terms: -4.5 + x = 11.842719282 Solving -4.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 11.842719282 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 11.842719282 + 4.5 x = 11.842719282 + 4.5 Combine like terms: 11.842719282 + 4.5 = 16.342719282 x = 16.342719282 Simplifying x = 16.342719282Subproblem 2
x + -4.5 = -11.842719282 Simplifying x + -4.5 = -11.842719282 Reorder the terms: -4.5 + x = -11.842719282 Solving -4.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -11.842719282 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -11.842719282 + 4.5 x = -11.842719282 + 4.5 Combine like terms: -11.842719282 + 4.5 = -7.342719282 x = -7.342719282 Simplifying x = -7.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.342719282, -7.342719282}
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