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Simplifying (8 + -2x)(8 + -2x) + -1x = 0 Multiply (8 + -2x) * (8 + -2x) (8(8 + -2x) + -2x * (8 + -2x)) + -1x = 0 ((8 * 8 + -2x * 8) + -2x * (8 + -2x)) + -1x = 0 ((64 + -16x) + -2x * (8 + -2x)) + -1x = 0 (64 + -16x + (8 * -2x + -2x * -2x)) + -1x = 0 (64 + -16x + (-16x + 4x2)) + -1x = 0 Combine like terms: -16x + -16x = -32x (64 + -32x + 4x2) + -1x = 0 Reorder the terms: 64 + -32x + -1x + 4x2 = 0 Combine like terms: -32x + -1x = -33x 64 + -33x + 4x2 = 0 Solving 64 + -33x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 16 + -8.25x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8.25x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -8.25x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8.25x + x2 = 0 + -16 -8.25x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8.25x + x2 = -16 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -16 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -16 + 17.015625 Combine like terms: -16 + 17.015625 = 1.015625 17.015625 + -8.25x + x2 = 1.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + -4.125) equal to 1.007782219 and -1.007782219.Subproblem 1
x + -4.125 = 1.007782219 Simplifying x + -4.125 = 1.007782219 Reorder the terms: -4.125 + x = 1.007782219 Solving -4.125 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 1.007782219 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 1.007782219 + 4.125 x = 1.007782219 + 4.125 Combine like terms: 1.007782219 + 4.125 = 5.132782219 x = 5.132782219 Simplifying x = 5.132782219Subproblem 2
x + -4.125 = -1.007782219 Simplifying x + -4.125 = -1.007782219 Reorder the terms: -4.125 + x = -1.007782219 Solving -4.125 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -1.007782219 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -1.007782219 + 4.125 x = -1.007782219 + 4.125 Combine like terms: -1.007782219 + 4.125 = 3.117217781 x = 3.117217781 Simplifying x = 3.117217781Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.132782219, 3.117217781}
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