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Simplifying (5x + -2)(2x + 8) = 180 Reorder the terms: (-2 + 5x)(2x + 8) = 180 Reorder the terms: (-2 + 5x)(8 + 2x) = 180 Multiply (-2 + 5x) * (8 + 2x) (-2(8 + 2x) + 5x * (8 + 2x)) = 180 ((8 * -2 + 2x * -2) + 5x * (8 + 2x)) = 180 ((-16 + -4x) + 5x * (8 + 2x)) = 180 (-16 + -4x + (8 * 5x + 2x * 5x)) = 180 (-16 + -4x + (40x + 10x2)) = 180 Combine like terms: -4x + 40x = 36x (-16 + 36x + 10x2) = 180 Solving -16 + 36x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -16 + -180 + 36x + 10x2 = 180 + -180 Combine like terms: -16 + -180 = -196 -196 + 36x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -196 + 36x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-98 + 18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-98 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying -98 + 18x + 5x2 = 0 Solving -98 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.6 + 3.6x + x2 = 0 Move the constant term to the right: Add '19.6' to each side of the equation. -19.6 + 3.6x + 19.6 + x2 = 0 + 19.6 Reorder the terms: -19.6 + 19.6 + 3.6x + x2 = 0 + 19.6 Combine like terms: -19.6 + 19.6 = 0.0 0.0 + 3.6x + x2 = 0 + 19.6 3.6x + x2 = 0 + 19.6 Combine like terms: 0 + 19.6 = 19.6 3.6x + x2 = 19.6 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 19.6 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 19.6 + 3.24 Combine like terms: 19.6 + 3.24 = 22.84 3.24 + 3.6x + x2 = 22.84 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 22.84 Calculate the square root of the right side: 4.779121258 Break this problem into two subproblems by setting (x + 1.8) equal to 4.779121258 and -4.779121258.Subproblem 1
x + 1.8 = 4.779121258 Simplifying x + 1.8 = 4.779121258 Reorder the terms: 1.8 + x = 4.779121258 Solving 1.8 + x = 4.779121258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 4.779121258 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 4.779121258 + -1.8 x = 4.779121258 + -1.8 Combine like terms: 4.779121258 + -1.8 = 2.979121258 x = 2.979121258 Simplifying x = 2.979121258Subproblem 2
x + 1.8 = -4.779121258 Simplifying x + 1.8 = -4.779121258 Reorder the terms: 1.8 + x = -4.779121258 Solving 1.8 + x = -4.779121258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -4.779121258 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -4.779121258 + -1.8 x = -4.779121258 + -1.8 Combine like terms: -4.779121258 + -1.8 = -6.579121258 x = -6.579121258 Simplifying x = -6.579121258Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.979121258, -6.579121258}Solution
x = {2.979121258, -6.579121258}
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