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Simplifying x2 + 4x + 50 + 4x + 31 = 180 Reorder the terms: 50 + 31 + 4x + 4x + x2 = 180 Combine like terms: 50 + 31 = 81 81 + 4x + 4x + x2 = 180 Combine like terms: 4x + 4x = 8x 81 + 8x + x2 = 180 Solving 81 + 8x + x2 = 180 Solving for variable 'x'. Reorder the terms: 81 + -180 + 8x + x2 = 180 + -180 Combine like terms: 81 + -180 = -99 -99 + 8x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -99 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 8x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 8x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 8x + x2 = 0 + 99 8x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 8x + x2 = 99 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 99 + 16 Reorder the terms: 16 + 8x + x2 = 99 + 16 Combine like terms: 99 + 16 = 115 16 + 8x + x2 = 115 Factor a perfect square on the left side: (x + 4)(x + 4) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + 4) equal to 10.723805295 and -10.723805295.Subproblem 1
x + 4 = 10.723805295 Simplifying x + 4 = 10.723805295 Reorder the terms: 4 + x = 10.723805295 Solving 4 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 10.723805295 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.723805295 + -4 x = 10.723805295 + -4 Combine like terms: 10.723805295 + -4 = 6.723805295 x = 6.723805295 Simplifying x = 6.723805295Subproblem 2
x + 4 = -10.723805295 Simplifying x + 4 = -10.723805295 Reorder the terms: 4 + x = -10.723805295 Solving 4 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -10.723805295 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.723805295 + -4 x = -10.723805295 + -4 Combine like terms: -10.723805295 + -4 = -14.723805295 x = -14.723805295 Simplifying x = -14.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.723805295, -14.723805295}
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