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Simplifying x2 + -10x + -61 = 0 Reorder the terms: -61 + -10x + x2 = 0 Solving -61 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + -10x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + -10x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -10x + x2 = 0 + 61 -10x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 -10x + x2 = 61 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 61 + 25 Reorder the terms: 25 + -10x + x2 = 61 + 25 Combine like terms: 61 + 25 = 86 25 + -10x + x2 = 86 Factor a perfect square on the left side: (x + -5)(x + -5) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -5) equal to 9.273618495 and -9.273618495.Subproblem 1
x + -5 = 9.273618495 Simplifying x + -5 = 9.273618495 Reorder the terms: -5 + x = 9.273618495 Solving -5 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 9.273618495 + 5 Combine like terms: -5 + 5 = 0 0 + x = 9.273618495 + 5 x = 9.273618495 + 5 Combine like terms: 9.273618495 + 5 = 14.273618495 x = 14.273618495 Simplifying x = 14.273618495Subproblem 2
x + -5 = -9.273618495 Simplifying x + -5 = -9.273618495 Reorder the terms: -5 + x = -9.273618495 Solving -5 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -9.273618495 + 5 Combine like terms: -5 + 5 = 0 0 + x = -9.273618495 + 5 x = -9.273618495 + 5 Combine like terms: -9.273618495 + 5 = -4.273618495 x = -4.273618495 Simplifying x = -4.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.273618495, -4.273618495}
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