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Simplifying x2 + -8x = 71 Reorder the terms: -8x + x2 = 71 Solving -8x + x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + -8x + x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -8x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -8x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -8x + x2 = 0 + 71 -8x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -8x + x2 = 71 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 71 + 16 Reorder the terms: 16 + -8x + x2 = 71 + 16 Combine like terms: 71 + 16 = 87 16 + -8x + x2 = 87 Factor a perfect square on the left side: (x + -4)(x + -4) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + -4) equal to 9.327379053 and -9.327379053.Subproblem 1
x + -4 = 9.327379053 Simplifying x + -4 = 9.327379053 Reorder the terms: -4 + x = 9.327379053 Solving -4 + x = 9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 9.327379053 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.327379053 + 4 x = 9.327379053 + 4 Combine like terms: 9.327379053 + 4 = 13.327379053 x = 13.327379053 Simplifying x = 13.327379053Subproblem 2
x + -4 = -9.327379053 Simplifying x + -4 = -9.327379053 Reorder the terms: -4 + x = -9.327379053 Solving -4 + x = -9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -9.327379053 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.327379053 + 4 x = -9.327379053 + 4 Combine like terms: -9.327379053 + 4 = -5.327379053 x = -5.327379053 Simplifying x = -5.327379053Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.327379053, -5.327379053}
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