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Simplifying 9x2 + 68x + 120 = 0 Reorder the terms: 120 + 68x + 9x2 = 0 Solving 120 + 68x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 13.33333333 + 7.555555556x + x2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + 7.555555556x + -13.33333333 + x2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + 7.555555556x + x2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + 7.555555556x + x2 = 0 + -13.33333333 7.555555556x + x2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 7.555555556x + x2 = -13.33333333 The x term is 7.555555556x. Take half its coefficient (3.777777778). Square it (14.27160494) and add it to both sides. Add '14.27160494' to each side of the equation. 7.555555556x + 14.27160494 + x2 = -13.33333333 + 14.27160494 Reorder the terms: 14.27160494 + 7.555555556x + x2 = -13.33333333 + 14.27160494 Combine like terms: -13.33333333 + 14.27160494 = 0.93827161 14.27160494 + 7.555555556x + x2 = 0.93827161 Factor a perfect square on the left side: (x + 3.777777778)(x + 3.777777778) = 0.93827161 Calculate the square root of the right side: 0.968644212 Break this problem into two subproblems by setting (x + 3.777777778) equal to 0.968644212 and -0.968644212.Subproblem 1
x + 3.777777778 = 0.968644212 Simplifying x + 3.777777778 = 0.968644212 Reorder the terms: 3.777777778 + x = 0.968644212 Solving 3.777777778 + x = 0.968644212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.777777778' to each side of the equation. 3.777777778 + -3.777777778 + x = 0.968644212 + -3.777777778 Combine like terms: 3.777777778 + -3.777777778 = 0.000000000 0.000000000 + x = 0.968644212 + -3.777777778 x = 0.968644212 + -3.777777778 Combine like terms: 0.968644212 + -3.777777778 = -2.809133566 x = -2.809133566 Simplifying x = -2.809133566Subproblem 2
x + 3.777777778 = -0.968644212 Simplifying x + 3.777777778 = -0.968644212 Reorder the terms: 3.777777778 + x = -0.968644212 Solving 3.777777778 + x = -0.968644212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.777777778' to each side of the equation. 3.777777778 + -3.777777778 + x = -0.968644212 + -3.777777778 Combine like terms: 3.777777778 + -3.777777778 = 0.000000000 0.000000000 + x = -0.968644212 + -3.777777778 x = -0.968644212 + -3.777777778 Combine like terms: -0.968644212 + -3.777777778 = -4.74642199 x = -4.74642199 Simplifying x = -4.74642199Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.809133566, -4.74642199}
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