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Simplifying 9x2 + -167x + 612 = 0 Reorder the terms: 612 + -167x + 9x2 = 0 Solving 612 + -167x + 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'. 68 + -18.55555556x + x2 = 0 Move the constant term to the right: Add '-68' to each side of the equation. 68 + -18.55555556x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + -18.55555556x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -18.55555556x + x2 = 0 + -68 -18.55555556x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 -18.55555556x + x2 = -68 The x term is -18.55555556x. Take half its coefficient (-9.27777778). Square it (86.07716054) and add it to both sides. Add '86.07716054' to each side of the equation. -18.55555556x + 86.07716054 + x2 = -68 + 86.07716054 Reorder the terms: 86.07716054 + -18.55555556x + x2 = -68 + 86.07716054 Combine like terms: -68 + 86.07716054 = 18.07716054 86.07716054 + -18.55555556x + x2 = 18.07716054 Factor a perfect square on the left side: (x + -9.27777778)(x + -9.27777778) = 18.07716054 Calculate the square root of the right side: 4.25172442 Break this problem into two subproblems by setting (x + -9.27777778) equal to 4.25172442 and -4.25172442.Subproblem 1
x + -9.27777778 = 4.25172442 Simplifying x + -9.27777778 = 4.25172442 Reorder the terms: -9.27777778 + x = 4.25172442 Solving -9.27777778 + x = 4.25172442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.27777778' to each side of the equation. -9.27777778 + 9.27777778 + x = 4.25172442 + 9.27777778 Combine like terms: -9.27777778 + 9.27777778 = 0.00000000 0.00000000 + x = 4.25172442 + 9.27777778 x = 4.25172442 + 9.27777778 Combine like terms: 4.25172442 + 9.27777778 = 13.5295022 x = 13.5295022 Simplifying x = 13.5295022Subproblem 2
x + -9.27777778 = -4.25172442 Simplifying x + -9.27777778 = -4.25172442 Reorder the terms: -9.27777778 + x = -4.25172442 Solving -9.27777778 + x = -4.25172442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.27777778' to each side of the equation. -9.27777778 + 9.27777778 + x = -4.25172442 + 9.27777778 Combine like terms: -9.27777778 + 9.27777778 = 0.00000000 0.00000000 + x = -4.25172442 + 9.27777778 x = -4.25172442 + 9.27777778 Combine like terms: -4.25172442 + 9.27777778 = 5.02605336 x = 5.02605336 Simplifying x = 5.02605336Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.5295022, 5.02605336}
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