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Simplifying x(x + -10) + -71 = (x + -1) Reorder the terms: x(-10 + x) + -71 = (x + -1) (-10 * x + x * x) + -71 = (x + -1) (-10x + x2) + -71 = (x + -1) Reorder the terms: -71 + -10x + x2 = (x + -1) Reorder the terms: -71 + -10x + x2 = (-1 + x) Remove parenthesis around (-1 + x) -71 + -10x + x2 = -1 + x Solving -71 + -10x + x2 = -1 + x Solving for variable 'x'. Reorder the terms: -71 + 1 + -10x + -1x + x2 = -1 + x + 1 + -1x Combine like terms: -71 + 1 = -70 -70 + -10x + -1x + x2 = -1 + x + 1 + -1x Combine like terms: -10x + -1x = -11x -70 + -11x + x2 = -1 + x + 1 + -1x Reorder the terms: -70 + -11x + x2 = -1 + 1 + x + -1x Combine like terms: -1 + 1 = 0 -70 + -11x + x2 = 0 + x + -1x -70 + -11x + x2 = x + -1x Combine like terms: x + -1x = 0 -70 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -11x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -11x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -11x + x2 = 0 + 70 -11x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -11x + x2 = 70 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 70 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 70 + 30.25 Combine like terms: 70 + 30.25 = 100.25 30.25 + -11x + x2 = 100.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -5.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -5.5 = 10.012492197 Simplifying x + -5.5 = 10.012492197 Reorder the terms: -5.5 + x = 10.012492197 Solving -5.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 10.012492197 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 10.012492197 + 5.5 x = 10.012492197 + 5.5 Combine like terms: 10.012492197 + 5.5 = 15.512492197 x = 15.512492197 Simplifying x = 15.512492197Subproblem 2
x + -5.5 = -10.012492197 Simplifying x + -5.5 = -10.012492197 Reorder the terms: -5.5 + x = -10.012492197 Solving -5.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -10.012492197 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -10.012492197 + 5.5 x = -10.012492197 + 5.5 Combine like terms: -10.012492197 + 5.5 = -4.512492197 x = -4.512492197 Simplifying x = -4.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.512492197, -4.512492197}
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