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Simplifying (8x + -7)(4x + -13) = 180 Reorder the terms: (-7 + 8x)(4x + -13) = 180 Reorder the terms: (-7 + 8x)(-13 + 4x) = 180 Multiply (-7 + 8x) * (-13 + 4x) (-7(-13 + 4x) + 8x * (-13 + 4x)) = 180 ((-13 * -7 + 4x * -7) + 8x * (-13 + 4x)) = 180 ((91 + -28x) + 8x * (-13 + 4x)) = 180 (91 + -28x + (-13 * 8x + 4x * 8x)) = 180 (91 + -28x + (-104x + 32x2)) = 180 Combine like terms: -28x + -104x = -132x (91 + -132x + 32x2) = 180 Solving 91 + -132x + 32x2 = 180 Solving for variable 'x'. Reorder the terms: 91 + -180 + -132x + 32x2 = 180 + -180 Combine like terms: 91 + -180 = -89 -89 + -132x + 32x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -89 + -132x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -2.78125 + -4.125x + x2 = 0 Move the constant term to the right: Add '2.78125' to each side of the equation. -2.78125 + -4.125x + 2.78125 + x2 = 0 + 2.78125 Reorder the terms: -2.78125 + 2.78125 + -4.125x + x2 = 0 + 2.78125 Combine like terms: -2.78125 + 2.78125 = 0.00000 0.00000 + -4.125x + x2 = 0 + 2.78125 -4.125x + x2 = 0 + 2.78125 Combine like terms: 0 + 2.78125 = 2.78125 -4.125x + x2 = 2.78125 The x term is -4.125x. Take half its coefficient (-2.0625). Square it (4.25390625) and add it to both sides. Add '4.25390625' to each side of the equation. -4.125x + 4.25390625 + x2 = 2.78125 + 4.25390625 Reorder the terms: 4.25390625 + -4.125x + x2 = 2.78125 + 4.25390625 Combine like terms: 2.78125 + 4.25390625 = 7.03515625 4.25390625 + -4.125x + x2 = 7.03515625 Factor a perfect square on the left side: (x + -2.0625)(x + -2.0625) = 7.03515625 Calculate the square root of the right side: 2.652386897 Break this problem into two subproblems by setting (x + -2.0625) equal to 2.652386897 and -2.652386897.Subproblem 1
x + -2.0625 = 2.652386897 Simplifying x + -2.0625 = 2.652386897 Reorder the terms: -2.0625 + x = 2.652386897 Solving -2.0625 + x = 2.652386897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = 2.652386897 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = 2.652386897 + 2.0625 x = 2.652386897 + 2.0625 Combine like terms: 2.652386897 + 2.0625 = 4.714886897 x = 4.714886897 Simplifying x = 4.714886897Subproblem 2
x + -2.0625 = -2.652386897 Simplifying x + -2.0625 = -2.652386897 Reorder the terms: -2.0625 + x = -2.652386897 Solving -2.0625 + x = -2.652386897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.0625' to each side of the equation. -2.0625 + 2.0625 + x = -2.652386897 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + x = -2.652386897 + 2.0625 x = -2.652386897 + 2.0625 Combine like terms: -2.652386897 + 2.0625 = -0.589886897 x = -0.589886897 Simplifying x = -0.589886897Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.714886897, -0.589886897}
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