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Simplifying (x2 + -8x) + (4x + 20) = 180 Reorder the terms: (-8x + x2) + (4x + 20) = 180 Remove parenthesis around (-8x + x2) -8x + x2 + (4x + 20) = 180 Reorder the terms: -8x + x2 + (20 + 4x) = 180 Remove parenthesis around (20 + 4x) -8x + x2 + 20 + 4x = 180 Reorder the terms: 20 + -8x + 4x + x2 = 180 Combine like terms: -8x + 4x = -4x 20 + -4x + x2 = 180 Solving 20 + -4x + x2 = 180 Solving for variable 'x'. Reorder the terms: 20 + -180 + -4x + x2 = 180 + -180 Combine like terms: 20 + -180 = -160 -160 + -4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -160 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -4x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -4x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -4x + x2 = 0 + 160 -4x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -4x + x2 = 160 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 160 + 4 Reorder the terms: 4 + -4x + x2 = 160 + 4 Combine like terms: 160 + 4 = 164 4 + -4x + x2 = 164 Factor a perfect square on the left side: (x + -2)(x + -2) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + -2) equal to 12.806248475 and -12.806248475.Subproblem 1
x + -2 = 12.806248475 Simplifying x + -2 = 12.806248475 Reorder the terms: -2 + x = 12.806248475 Solving -2 + x = 12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.806248475 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.806248475 + 2 x = 12.806248475 + 2 Combine like terms: 12.806248475 + 2 = 14.806248475 x = 14.806248475 Simplifying x = 14.806248475Subproblem 2
x + -2 = -12.806248475 Simplifying x + -2 = -12.806248475 Reorder the terms: -2 + x = -12.806248475 Solving -2 + x = -12.806248475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.806248475 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.806248475 + 2 x = -12.806248475 + 2 Combine like terms: -12.806248475 + 2 = -10.806248475 x = -10.806248475 Simplifying x = -10.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.806248475, -10.806248475}
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