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Simplifying -1(x + -8) + 4x = 2(x + 4) * x Reorder the terms: -1(-8 + x) + 4x = 2(x + 4) * x (-8 * -1 + x * -1) + 4x = 2(x + 4) * x (8 + -1x) + 4x = 2(x + 4) * x Combine like terms: -1x + 4x = 3x 8 + 3x = 2(x + 4) * x Reorder the terms: 8 + 3x = 2(4 + x) * x Reorder the terms for easier multiplication: 8 + 3x = 2x(4 + x) 8 + 3x = (4 * 2x + x * 2x) 8 + 3x = (8x + 2x2) Solving 8 + 3x = 8x + 2x2 Solving for variable 'x'. Combine like terms: 3x + -8x = -5x 8 + -5x + -2x2 = 8x + 2x2 + -8x + -2x2 Reorder the terms: 8 + -5x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 8 + -5x + -2x2 = 0 + 2x2 + -2x2 8 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + 2.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.5x + x2 = 0 + 4 2.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.5x + x2 = 4 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 4 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 4 + 1.5625 Combine like terms: 4 + 1.5625 = 5.5625 1.5625 + 2.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + 1.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + 1.25 = 2.358495283 Simplifying x + 1.25 = 2.358495283 Reorder the terms: 1.25 + x = 2.358495283 Solving 1.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.358495283 + -1.25 x = 2.358495283 + -1.25 Combine like terms: 2.358495283 + -1.25 = 1.108495283 x = 1.108495283 Simplifying x = 1.108495283Subproblem 2
x + 1.25 = -2.358495283 Simplifying x + 1.25 = -2.358495283 Reorder the terms: 1.25 + x = -2.358495283 Solving 1.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.358495283 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.358495283 + -1.25 x = -2.358495283 + -1.25 Combine like terms: -2.358495283 + -1.25 = -3.608495283 x = -3.608495283 Simplifying x = -3.608495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.108495283, -3.608495283}
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