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Simplifying -5(x + 3)(x + 8) = x Reorder the terms: -5(3 + x)(x + 8) = x Reorder the terms: -5(3 + x)(8 + x) = x Multiply (3 + x) * (8 + x) -5(3(8 + x) + x(8 + x)) = x -5((8 * 3 + x * 3) + x(8 + x)) = x -5((24 + 3x) + x(8 + x)) = x -5(24 + 3x + (8 * x + x * x)) = x -5(24 + 3x + (8x + x2)) = x Combine like terms: 3x + 8x = 11x -5(24 + 11x + x2) = x (24 * -5 + 11x * -5 + x2 * -5) = x (-120 + -55x + -5x2) = x Solving -120 + -55x + -5x2 = x Solving for variable 'x'. Reorder the terms: -120 + -55x + -1x + -5x2 = x + -1x Combine like terms: -55x + -1x = -56x -120 + -56x + -5x2 = x + -1x Combine like terms: x + -1x = 0 -120 + -56x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(120 + 56x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(120 + 56x + 5x2)' equal to zero and attempt to solve: Simplifying 120 + 56x + 5x2 = 0 Solving 120 + 56x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 24 + 11.2x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 11.2x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 11.2x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 11.2x + x2 = 0 + -24 11.2x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 11.2x + x2 = -24 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = -24 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = -24 + 31.36 Combine like terms: -24 + 31.36 = 7.36 31.36 + 11.2x + x2 = 7.36 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (x + 5.6) equal to 2.712931993 and -2.712931993.Subproblem 1
x + 5.6 = 2.712931993 Simplifying x + 5.6 = 2.712931993 Reorder the terms: 5.6 + x = 2.712931993 Solving 5.6 + x = 2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 2.712931993 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 2.712931993 + -5.6 x = 2.712931993 + -5.6 Combine like terms: 2.712931993 + -5.6 = -2.887068007 x = -2.887068007 Simplifying x = -2.887068007Subproblem 2
x + 5.6 = -2.712931993 Simplifying x + 5.6 = -2.712931993 Reorder the terms: 5.6 + x = -2.712931993 Solving 5.6 + x = -2.712931993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -2.712931993 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -2.712931993 + -5.6 x = -2.712931993 + -5.6 Combine like terms: -2.712931993 + -5.6 = -8.312931993 x = -8.312931993 Simplifying x = -8.312931993Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.887068007, -8.312931993}Solution
x = {-2.887068007, -8.312931993}
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