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Simplifying 12(x + 56) * 45(x) = 52 Reorder the terms: 12(56 + x) * 45(x) = 52 Reorder the terms for easier multiplication: 12 * 45x(56 + x) = 52 Multiply 12 * 45 540x(56 + x) = 52 (56 * 540x + x * 540x) = 52 (30240x + 540x2) = 52 Solving 30240x + 540x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 30240x + 540x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 30240x + 540x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-13 + 7560x + 135x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-13 + 7560x + 135x2)' equal to zero and attempt to solve: Simplifying -13 + 7560x + 135x2 = 0 Solving -13 + 7560x + 135x2 = 0 Begin completing the square. Divide all terms by 135 the coefficient of the squared term: Divide each side by '135'. -0.0962962963 + 56x + x2 = 0 Move the constant term to the right: Add '0.0962962963' to each side of the equation. -0.0962962963 + 56x + 0.0962962963 + x2 = 0 + 0.0962962963 Reorder the terms: -0.0962962963 + 0.0962962963 + 56x + x2 = 0 + 0.0962962963 Combine like terms: -0.0962962963 + 0.0962962963 = 0.0000000000 0.0000000000 + 56x + x2 = 0 + 0.0962962963 56x + x2 = 0 + 0.0962962963 Combine like terms: 0 + 0.0962962963 = 0.0962962963 56x + x2 = 0.0962962963 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = 0.0962962963 + 784 Reorder the terms: 784 + 56x + x2 = 0.0962962963 + 784 Combine like terms: 0.0962962963 + 784 = 784.0962962963 784 + 56x + x2 = 784.0962962963 Factor a perfect square on the left side: (x + 28)(x + 28) = 784.0962962963 Calculate the square root of the right side: 28.001719524 Break this problem into two subproblems by setting (x + 28) equal to 28.001719524 and -28.001719524.Subproblem 1
x + 28 = 28.001719524 Simplifying x + 28 = 28.001719524 Reorder the terms: 28 + x = 28.001719524 Solving 28 + x = 28.001719524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 28.001719524 + -28 Combine like terms: 28 + -28 = 0 0 + x = 28.001719524 + -28 x = 28.001719524 + -28 Combine like terms: 28.001719524 + -28 = 0.001719524 x = 0.001719524 Simplifying x = 0.001719524Subproblem 2
x + 28 = -28.001719524 Simplifying x + 28 = -28.001719524 Reorder the terms: 28 + x = -28.001719524 Solving 28 + x = -28.001719524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -28.001719524 + -28 Combine like terms: 28 + -28 = 0 0 + x = -28.001719524 + -28 x = -28.001719524 + -28 Combine like terms: -28.001719524 + -28 = -56.001719524 x = -56.001719524 Simplifying x = -56.001719524Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001719524, -56.001719524}Solution
x = {0.001719524, -56.001719524}
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