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Simplifying (x + 2)(4x + -137) = 180 Reorder the terms: (2 + x)(4x + -137) = 180 Reorder the terms: (2 + x)(-137 + 4x) = 180 Multiply (2 + x) * (-137 + 4x) (2(-137 + 4x) + x(-137 + 4x)) = 180 ((-137 * 2 + 4x * 2) + x(-137 + 4x)) = 180 ((-274 + 8x) + x(-137 + 4x)) = 180 (-274 + 8x + (-137 * x + 4x * x)) = 180 (-274 + 8x + (-137x + 4x2)) = 180 Combine like terms: 8x + -137x = -129x (-274 + -129x + 4x2) = 180 Solving -274 + -129x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -274 + -180 + -129x + 4x2 = 180 + -180 Combine like terms: -274 + -180 = -454 -454 + -129x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -454 + -129x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -113.5 + -32.25x + x2 = 0 Move the constant term to the right: Add '113.5' to each side of the equation. -113.5 + -32.25x + 113.5 + x2 = 0 + 113.5 Reorder the terms: -113.5 + 113.5 + -32.25x + x2 = 0 + 113.5 Combine like terms: -113.5 + 113.5 = 0.0 0.0 + -32.25x + x2 = 0 + 113.5 -32.25x + x2 = 0 + 113.5 Combine like terms: 0 + 113.5 = 113.5 -32.25x + x2 = 113.5 The x term is -32.25x. Take half its coefficient (-16.125). Square it (260.015625) and add it to both sides. Add '260.015625' to each side of the equation. -32.25x + 260.015625 + x2 = 113.5 + 260.015625 Reorder the terms: 260.015625 + -32.25x + x2 = 113.5 + 260.015625 Combine like terms: 113.5 + 260.015625 = 373.515625 260.015625 + -32.25x + x2 = 373.515625 Factor a perfect square on the left side: (x + -16.125)(x + -16.125) = 373.515625 Calculate the square root of the right side: 19.326552331 Break this problem into two subproblems by setting (x + -16.125) equal to 19.326552331 and -19.326552331.Subproblem 1
x + -16.125 = 19.326552331 Simplifying x + -16.125 = 19.326552331 Reorder the terms: -16.125 + x = 19.326552331 Solving -16.125 + x = 19.326552331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.125' to each side of the equation. -16.125 + 16.125 + x = 19.326552331 + 16.125 Combine like terms: -16.125 + 16.125 = 0.000 0.000 + x = 19.326552331 + 16.125 x = 19.326552331 + 16.125 Combine like terms: 19.326552331 + 16.125 = 35.451552331 x = 35.451552331 Simplifying x = 35.451552331Subproblem 2
x + -16.125 = -19.326552331 Simplifying x + -16.125 = -19.326552331 Reorder the terms: -16.125 + x = -19.326552331 Solving -16.125 + x = -19.326552331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.125' to each side of the equation. -16.125 + 16.125 + x = -19.326552331 + 16.125 Combine like terms: -16.125 + 16.125 = 0.000 0.000 + x = -19.326552331 + 16.125 x = -19.326552331 + 16.125 Combine like terms: -19.326552331 + 16.125 = -3.201552331 x = -3.201552331 Simplifying x = -3.201552331Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.451552331, -3.201552331}
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