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Simplifying 2x2 + -10x + -117 = 0 Reorder the terms: -117 + -10x + 2x2 = 0 Solving -117 + -10x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -58.5 + -5x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + -5x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + -5x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + -5x + x2 = 0 + 58.5 -5x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 -5x + x2 = 58.5 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 = 58.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 58.5 + 6.25 Combine like terms: 58.5 + 6.25 = 64.75 6.25 + -5x + x2 = 64.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 64.75 Calculate the square root of the right side: 8.04673847 Break this problem into two subproblems by setting (x + -2.5) equal to 8.04673847 and -8.04673847.Subproblem 1
x + -2.5 = 8.04673847 Simplifying x + -2.5 = 8.04673847 Reorder the terms: -2.5 + x = 8.04673847 Solving -2.5 + x = 8.04673847 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 = 8.04673847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 8.04673847 + 2.5 x = 8.04673847 + 2.5 Combine like terms: 8.04673847 + 2.5 = 10.54673847 x = 10.54673847 Simplifying x = 10.54673847Subproblem 2
x + -2.5 = -8.04673847 Simplifying x + -2.5 = -8.04673847 Reorder the terms: -2.5 + x = -8.04673847 Solving -2.5 + x = -8.04673847 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 = -8.04673847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -8.04673847 + 2.5 x = -8.04673847 + 2.5 Combine like terms: -8.04673847 + 2.5 = -5.54673847 x = -5.54673847 Simplifying x = -5.54673847Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.54673847, -5.54673847}
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