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Simplifying (x + -2(3))(x + -3(4)) = 5(24) Multiply -2 * 3 (x + -6)(x + -3(4)) = 5(24) Reorder the terms: (-6 + x)(x + -3(4)) = 5(24) Multiply -3 * 4 (-6 + x)(x + -12) = 5(24) Reorder the terms: (-6 + x)(-12 + x) = 5(24) Multiply (-6 + x) * (-12 + x) (-6(-12 + x) + x(-12 + x)) = 5(24) ((-12 * -6 + x * -6) + x(-12 + x)) = 5(24) ((72 + -6x) + x(-12 + x)) = 5(24) (72 + -6x + (-12 * x + x * x)) = 5(24) (72 + -6x + (-12x + x2)) = 5(24) Combine like terms: -6x + -12x = -18x (72 + -18x + x2) = 5(24) Multiply 5 * 24 72 + -18x + x2 = 120 Solving 72 + -18x + x2 = 120 Solving for variable 'x'. Reorder the terms: 72 + -120 + -18x + x2 = 120 + -120 Combine like terms: 72 + -120 = -48 -48 + -18x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -48 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -18x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -18x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -18x + x2 = 0 + 48 -18x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -18x + x2 = 48 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 48 + 81 Reorder the terms: 81 + -18x + x2 = 48 + 81 Combine like terms: 48 + 81 = 129 81 + -18x + x2 = 129 Factor a perfect square on the left side: (x + -9)(x + -9) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -9) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -9 = 11.357816692 Simplifying x + -9 = 11.357816692 Reorder the terms: -9 + x = 11.357816692 Solving -9 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + x = 11.357816692 + 9 x = 11.357816692 + 9 Combine like terms: 11.357816692 + 9 = 20.357816692 x = 20.357816692 Simplifying x = 20.357816692Subproblem 2
x + -9 = -11.357816692 Simplifying x + -9 = -11.357816692 Reorder the terms: -9 + x = -11.357816692 Solving -9 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -11.357816692 + 9 Combine like terms: -9 + 9 = 0 0 + x = -11.357816692 + 9 x = -11.357816692 + 9 Combine like terms: -11.357816692 + 9 = -2.357816692 x = -2.357816692 Simplifying x = -2.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.357816692, -2.357816692}
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