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Simplifying (8 + -1x)(8 + -1x) = 40 Multiply (8 + -1x) * (8 + -1x) (8(8 + -1x) + -1x * (8 + -1x)) = 40 ((8 * 8 + -1x * 8) + -1x * (8 + -1x)) = 40 ((64 + -8x) + -1x * (8 + -1x)) = 40 (64 + -8x + (8 * -1x + -1x * -1x)) = 40 (64 + -8x + (-8x + 1x2)) = 40 Combine like terms: -8x + -8x = -16x (64 + -16x + 1x2) = 40 Solving 64 + -16x + 1x2 = 40 Solving for variable 'x'. Reorder the terms: 64 + -40 + -16x + 1x2 = 40 + -40 Combine like terms: 64 + -40 = 24 24 + -16x + 1x2 = 40 + -40 Combine like terms: 40 + -40 = 0 24 + -16x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -16x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -16x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -16x + x2 = 0 + -24 -16x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -16x + x2 = -24 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -24 + 64 Reorder the terms: 64 + -16x + x2 = -24 + 64 Combine like terms: -24 + 64 = 40 64 + -16x + x2 = 40 Factor a perfect square on the left side: (x + -8)(x + -8) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -8) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -8 = 6.32455532 Simplifying x + -8 = 6.32455532 Reorder the terms: -8 + x = 6.32455532 Solving -8 + x = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.32455532 + 8 x = 6.32455532 + 8 Combine like terms: 6.32455532 + 8 = 14.32455532 x = 14.32455532 Simplifying x = 14.32455532Subproblem 2
x + -8 = -6.32455532 Simplifying x + -8 = -6.32455532 Reorder the terms: -8 + x = -6.32455532 Solving -8 + x = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -6.32455532 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.32455532 + 8 x = -6.32455532 + 8 Combine like terms: -6.32455532 + 8 = 1.67544468 x = 1.67544468 Simplifying x = 1.67544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.32455532, 1.67544468}
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