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Simplifying -114 + -8x = 11 + -8(x)(x) Multiply x * x -114 + -8x = 11 + -8x2 Solving -114 + -8x = 11 + -8x2 Solving for variable 'x'. Reorder the terms: -114 + -11 + -8x + 8x2 = 11 + -8x2 + -11 + 8x2 Combine like terms: -114 + -11 = -125 -125 + -8x + 8x2 = 11 + -8x2 + -11 + 8x2 Reorder the terms: -125 + -8x + 8x2 = 11 + -11 + -8x2 + 8x2 Combine like terms: 11 + -11 = 0 -125 + -8x + 8x2 = 0 + -8x2 + 8x2 -125 + -8x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -125 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15.625 + -1x + x2 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + -1x + 15.625 + x2 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + -1x + x2 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + -1x + x2 = 0 + 15.625 -1x + x2 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 -1x + x2 = 15.625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 15.625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 15.625 + 0.25 Combine like terms: 15.625 + 0.25 = 15.875 0.25 + -1x + x2 = 15.875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 15.875 Calculate the square root of the right side: 3.984344363 Break this problem into two subproblems by setting (x + -0.5) equal to 3.984344363 and -3.984344363.Subproblem 1
x + -0.5 = 3.984344363 Simplifying x + -0.5 = 3.984344363 Reorder the terms: -0.5 + x = 3.984344363 Solving -0.5 + x = 3.984344363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.984344363 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.984344363 + 0.5 x = 3.984344363 + 0.5 Combine like terms: 3.984344363 + 0.5 = 4.484344363 x = 4.484344363 Simplifying x = 4.484344363Subproblem 2
x + -0.5 = -3.984344363 Simplifying x + -0.5 = -3.984344363 Reorder the terms: -0.5 + x = -3.984344363 Solving -0.5 + x = -3.984344363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.984344363 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.984344363 + 0.5 x = -3.984344363 + 0.5 Combine like terms: -3.984344363 + 0.5 = -3.484344363 x = -3.484344363 Simplifying x = -3.484344363Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.484344363, -3.484344363}
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