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Simplifying x2 + -71 = 10x Reorder the terms: -71 + x2 = 10x Solving -71 + x2 = 10x Solving for variable 'x'. Reorder the terms: -71 + -10x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -71 + -10x + x2 = 0 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 = 14.797958971 x = 14.797958971 Simplifying x = 14.797958971Subproblem 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 = -4.797958971 x = -4.797958971 Simplifying x = -4.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.797958971, -4.797958971}
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