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Simplifying 169 = 2x2 + -10x Reorder the terms: 169 = -10x + 2x2 Solving 169 = -10x + 2x2 Solving for variable 'x'. Reorder the terms: 169 + 10x + -2x2 = -10x + 10x + 2x2 + -2x2 Combine like terms: -10x + 10x = 0 169 + 10x + -2x2 = 0 + 2x2 + -2x2 169 + 10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 169 + 10x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -84.5 + -5x + x2 = 0 Move the constant term to the right: Add '84.5' to each side of the equation. -84.5 + -5x + 84.5 + x2 = 0 + 84.5 Reorder the terms: -84.5 + 84.5 + -5x + x2 = 0 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + -5x + x2 = 0 + 84.5 -5x + x2 = 0 + 84.5 Combine like terms: 0 + 84.5 = 84.5 -5x + x2 = 84.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 84.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 84.5 + 6.25 Combine like terms: 84.5 + 6.25 = 90.75 6.25 + -5x + x2 = 90.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 90.75 Calculate the square root of the right side: 9.526279442 Break this problem into two subproblems by setting (x + -2.5) equal to 9.526279442 and -9.526279442.Subproblem 1
x + -2.5 = 9.526279442 Simplifying x + -2.5 = 9.526279442 Reorder the terms: -2.5 + x = 9.526279442 Solving -2.5 + x = 9.526279442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 9.526279442 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 9.526279442 + 2.5 x = 9.526279442 + 2.5 Combine like terms: 9.526279442 + 2.5 = 12.026279442 x = 12.026279442 Simplifying x = 12.026279442Subproblem 2
x + -2.5 = -9.526279442 Simplifying x + -2.5 = -9.526279442 Reorder the terms: -2.5 + x = -9.526279442 Solving -2.5 + x = -9.526279442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -9.526279442 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -9.526279442 + 2.5 x = -9.526279442 + 2.5 Combine like terms: -9.526279442 + 2.5 = -7.026279442 x = -7.026279442 Simplifying x = -7.026279442Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.026279442, -7.026279442}
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