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Simplifying x2 + 10x + -71 = 0 Reorder the terms: -71 + 10x + x2 = 0 Solving -71 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 10x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 10x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 10x + x2 = 0 + 71 10x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 10x + x2 = 71 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 = 71 + 25 Reorder the terms: 25 + 10x + x2 = 71 + 25 Combine like terms: 71 + 25 = 96 25 + 10x + x2 = 96 Factor a perfect square on the left side: (x + 5)(x + 5) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 5) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 5 = 9.797958971 Simplifying x + 5 = 9.797958971 Reorder the terms: 5 + x = 9.797958971 Solving 5 + x = 9.797958971 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 = 9.797958971 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.797958971 + -5 x = 9.797958971 + -5 Combine like terms: 9.797958971 + -5 = 4.797958971 x = 4.797958971 Simplifying x = 4.797958971Subproblem 2
x + 5 = -9.797958971 Simplifying x + 5 = -9.797958971 Reorder the terms: 5 + x = -9.797958971 Solving 5 + x = -9.797958971 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 = -9.797958971 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.797958971 + -5 x = -9.797958971 + -5 Combine like terms: -9.797958971 + -5 = -14.797958971 x = -14.797958971 Simplifying x = -14.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.797958971, -14.797958971}
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