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Simplifying -8x(x + -4) + 5x + -3 = 2(x + -4) Reorder the terms: -8x(-4 + x) + 5x + -3 = 2(x + -4) (-4 * -8x + x * -8x) + 5x + -3 = 2(x + -4) (32x + -8x2) + 5x + -3 = 2(x + -4) Reorder the terms: -3 + 32x + 5x + -8x2 = 2(x + -4) Combine like terms: 32x + 5x = 37x -3 + 37x + -8x2 = 2(x + -4) Reorder the terms: -3 + 37x + -8x2 = 2(-4 + x) -3 + 37x + -8x2 = (-4 * 2 + x * 2) -3 + 37x + -8x2 = (-8 + 2x) Solving -3 + 37x + -8x2 = -8 + 2x Solving for variable 'x'. Reorder the terms: -3 + 8 + 37x + -2x + -8x2 = -8 + 2x + 8 + -2x Combine like terms: -3 + 8 = 5 5 + 37x + -2x + -8x2 = -8 + 2x + 8 + -2x Combine like terms: 37x + -2x = 35x 5 + 35x + -8x2 = -8 + 2x + 8 + -2x Reorder the terms: 5 + 35x + -8x2 = -8 + 8 + 2x + -2x Combine like terms: -8 + 8 = 0 5 + 35x + -8x2 = 0 + 2x + -2x 5 + 35x + -8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 5 + 35x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -4.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -4.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -4.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -4.375x + x2 = 0 + 0.625 -4.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -4.375x + x2 = 0.625 The x term is -4.375x. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375x + 4.78515625 + x2 = 0.625 + 4.78515625 Reorder the terms: 4.78515625 + -4.375x + x2 = 0.625 + 4.78515625 Combine like terms: 0.625 + 4.78515625 = 5.41015625 4.78515625 + -4.375x + x2 = 5.41015625 Factor a perfect square on the left side: (x + -2.1875)(x + -2.1875) = 5.41015625 Calculate the square root of the right side: 2.325974258 Break this problem into two subproblems by setting (x + -2.1875) equal to 2.325974258 and -2.325974258.Subproblem 1
x + -2.1875 = 2.325974258 Simplifying x + -2.1875 = 2.325974258 Reorder the terms: -2.1875 + x = 2.325974258 Solving -2.1875 + x = 2.325974258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = 2.325974258 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = 2.325974258 + 2.1875 x = 2.325974258 + 2.1875 Combine like terms: 2.325974258 + 2.1875 = 4.513474258 x = 4.513474258 Simplifying x = 4.513474258Subproblem 2
x + -2.1875 = -2.325974258 Simplifying x + -2.1875 = -2.325974258 Reorder the terms: -2.1875 + x = -2.325974258 Solving -2.1875 + x = -2.325974258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + x = -2.325974258 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + x = -2.325974258 + 2.1875 x = -2.325974258 + 2.1875 Combine like terms: -2.325974258 + 2.1875 = -0.138474258 x = -0.138474258 Simplifying x = -0.138474258Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.513474258, -0.138474258}
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