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Simplifying 4x(2x + 12) = 180 Reorder the terms: 4x(12 + 2x) = 180 (12 * 4x + 2x * 4x) = 180 (48x + 8x2) = 180 Solving 48x + 8x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 48x + 8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 48x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 12x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying -45 + 12x + 2x2 = 0 Solving -45 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 6x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 6x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 6x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 6x + x2 = 0 + 22.5 6x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 6x + x2 = 22.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 22.5 + 9 Reorder the terms: 9 + 6x + x2 = 22.5 + 9 Combine like terms: 22.5 + 9 = 31.5 9 + 6x + x2 = 31.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 31.5 Calculate the square root of the right side: 5.61248608 Break this problem into two subproblems by setting (x + 3) equal to 5.61248608 and -5.61248608.Subproblem 1
x + 3 = 5.61248608 Simplifying x + 3 = 5.61248608 Reorder the terms: 3 + x = 5.61248608 Solving 3 + x = 5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.61248608 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.61248608 + -3 x = 5.61248608 + -3 Combine like terms: 5.61248608 + -3 = 2.61248608 x = 2.61248608 Simplifying x = 2.61248608Subproblem 2
x + 3 = -5.61248608 Simplifying x + 3 = -5.61248608 Reorder the terms: 3 + x = -5.61248608 Solving 3 + x = -5.61248608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.61248608 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.61248608 + -3 x = -5.61248608 + -3 Combine like terms: -5.61248608 + -3 = -8.61248608 x = -8.61248608 Simplifying x = -8.61248608Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.61248608, -8.61248608}Solution
x = {2.61248608, -8.61248608}
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