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Simplifying 9x2 + 9x + -124 = 0 Reorder the terms: -124 + 9x + 9x2 = 0 Solving -124 + 9x + 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'. -13.77777778 + x + x2 = 0 Move the constant term to the right: Add '13.77777778' to each side of the equation. -13.77777778 + x + 13.77777778 + x2 = 0 + 13.77777778 Reorder the terms: -13.77777778 + 13.77777778 + x + x2 = 0 + 13.77777778 Combine like terms: -13.77777778 + 13.77777778 = 0.00000000 0.00000000 + x + x2 = 0 + 13.77777778 x + x2 = 0 + 13.77777778 Combine like terms: 0 + 13.77777778 = 13.77777778 x + x2 = 13.77777778 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 13.77777778 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 13.77777778 + 0.25 Combine like terms: 13.77777778 + 0.25 = 14.02777778 1.25 + x2 = 14.02777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14.02777778 Calculate the square root of the right side: 3.745367509 Break this problem into two subproblems by setting (x + 0.5) equal to 3.745367509 and -3.745367509.Subproblem 1
x + 0.5 = 3.745367509 Simplifying x + 0.5 = 3.745367509 Reorder the terms: 0.5 + x = 3.745367509 Solving 0.5 + x = 3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.745367509 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.745367509 + -0.5 x = 3.745367509 + -0.5 Combine like terms: 3.745367509 + -0.5 = 3.245367509 x = 3.245367509 Simplifying x = 3.245367509Subproblem 2
x + 0.5 = -3.745367509 Simplifying x + 0.5 = -3.745367509 Reorder the terms: 0.5 + x = -3.745367509 Solving 0.5 + x = -3.745367509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.745367509 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.745367509 + -0.5 x = -3.745367509 + -0.5 Combine like terms: -3.745367509 + -0.5 = -4.245367509 x = -4.245367509 Simplifying x = -4.245367509Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.245367509, -4.245367509}
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