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Simplifying (x + 5) + (x + 5)(4x + -4) = 180 Reorder the terms: (5 + x) + (x + 5)(4x + -4) = 180 Remove parenthesis around (5 + x) 5 + x + (x + 5)(4x + -4) = 180 Reorder the terms: 5 + x + (5 + x)(4x + -4) = 180 Reorder the terms: 5 + x + (5 + x)(-4 + 4x) = 180 Multiply (5 + x) * (-4 + 4x) 5 + x + (5(-4 + 4x) + x(-4 + 4x)) = 180 5 + x + ((-4 * 5 + 4x * 5) + x(-4 + 4x)) = 180 5 + x + ((-20 + 20x) + x(-4 + 4x)) = 180 5 + x + (-20 + 20x + (-4 * x + 4x * x)) = 180 5 + x + (-20 + 20x + (-4x + 4x2)) = 180 Combine like terms: 20x + -4x = 16x 5 + x + (-20 + 16x + 4x2) = 180 Reorder the terms: 5 + -20 + x + 16x + 4x2 = 180 Combine like terms: 5 + -20 = -15 -15 + x + 16x + 4x2 = 180 Combine like terms: x + 16x = 17x -15 + 17x + 4x2 = 180 Solving -15 + 17x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -15 + -180 + 17x + 4x2 = 180 + -180 Combine like terms: -15 + -180 = -195 -195 + 17x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -195 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -48.75 + 4.25x + x2 = 0 Move the constant term to the right: Add '48.75' to each side of the equation. -48.75 + 4.25x + 48.75 + x2 = 0 + 48.75 Reorder the terms: -48.75 + 48.75 + 4.25x + x2 = 0 + 48.75 Combine like terms: -48.75 + 48.75 = 0.00 0.00 + 4.25x + x2 = 0 + 48.75 4.25x + x2 = 0 + 48.75 Combine like terms: 0 + 48.75 = 48.75 4.25x + x2 = 48.75 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 48.75 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 48.75 + 4.515625 Combine like terms: 48.75 + 4.515625 = 53.265625 4.515625 + 4.25x + x2 = 53.265625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 53.265625 Calculate the square root of the right side: 7.298330288 Break this problem into two subproblems by setting (x + 2.125) equal to 7.298330288 and -7.298330288.Subproblem 1
x + 2.125 = 7.298330288 Simplifying x + 2.125 = 7.298330288 Reorder the terms: 2.125 + x = 7.298330288 Solving 2.125 + x = 7.298330288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 7.298330288 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 7.298330288 + -2.125 x = 7.298330288 + -2.125 Combine like terms: 7.298330288 + -2.125 = 5.173330288 x = 5.173330288 Simplifying x = 5.173330288Subproblem 2
x + 2.125 = -7.298330288 Simplifying x + 2.125 = -7.298330288 Reorder the terms: 2.125 + x = -7.298330288 Solving 2.125 + x = -7.298330288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -7.298330288 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -7.298330288 + -2.125 x = -7.298330288 + -2.125 Combine like terms: -7.298330288 + -2.125 = -9.423330288 x = -9.423330288 Simplifying x = -9.423330288Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.173330288, -9.423330288}
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