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Simplifying (5x + 10)(2x + -12) = 180 Reorder the terms: (10 + 5x)(2x + -12) = 180 Reorder the terms: (10 + 5x)(-12 + 2x) = 180 Multiply (10 + 5x) * (-12 + 2x) (10(-12 + 2x) + 5x * (-12 + 2x)) = 180 ((-12 * 10 + 2x * 10) + 5x * (-12 + 2x)) = 180 ((-120 + 20x) + 5x * (-12 + 2x)) = 180 (-120 + 20x + (-12 * 5x + 2x * 5x)) = 180 (-120 + 20x + (-60x + 10x2)) = 180 Combine like terms: 20x + -60x = -40x (-120 + -40x + 10x2) = 180 Solving -120 + -40x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -120 + -180 + -40x + 10x2 = 180 + -180 Combine like terms: -120 + -180 = -300 -300 + -40x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -300 + -40x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-30 + -4x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-30 + -4x + x2)' equal to zero and attempt to solve: Simplifying -30 + -4x + x2 = 0 Solving -30 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -4x + x2 = 0 + 30 -4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -4x + x2 = 30 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 30 + 4 Reorder the terms: 4 + -4x + x2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + -4x + x2 = 34 Factor a perfect square on the left side: (x + -2)(x + -2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -2) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -2 = 5.830951895 Simplifying x + -2 = 5.830951895 Reorder the terms: -2 + x = 5.830951895 Solving -2 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.830951895 + 2 x = 5.830951895 + 2 Combine like terms: 5.830951895 + 2 = 7.830951895 x = 7.830951895 Simplifying x = 7.830951895Subproblem 2
x + -2 = -5.830951895 Simplifying x + -2 = -5.830951895 Reorder the terms: -2 + x = -5.830951895 Solving -2 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.830951895 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.830951895 + 2 x = -5.830951895 + 2 Combine like terms: -5.830951895 + 2 = -3.830951895 x = -3.830951895 Simplifying x = -3.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.830951895, -3.830951895}Solution
x = {7.830951895, -3.830951895}
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