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Simplifying x2 + 8x + 16 = 180 Reorder the terms: 16 + 8x + x2 = 180 Solving 16 + 8x + x2 = 180 Solving for variable 'x'. Reorder the terms: 16 + -180 + 8x + x2 = 180 + -180 Combine like terms: 16 + -180 = -164 -164 + 8x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -164 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '164' to each side of the equation. -164 + 8x + 164 + x2 = 0 + 164 Reorder the terms: -164 + 164 + 8x + x2 = 0 + 164 Combine like terms: -164 + 164 = 0 0 + 8x + x2 = 0 + 164 8x + x2 = 0 + 164 Combine like terms: 0 + 164 = 164 8x + x2 = 164 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 = 164 + 16 Reorder the terms: 16 + 8x + x2 = 164 + 16 Combine like terms: 164 + 16 = 180 16 + 8x + x2 = 180 Factor a perfect square on the left side: (x + 4)(x + 4) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 4) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 4 = 13.416407865 Simplifying x + 4 = 13.416407865 Reorder the terms: 4 + x = 13.416407865 Solving 4 + x = 13.416407865 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 = 13.416407865 + -4 Combine like terms: 4 + -4 = 0 0 + x = 13.416407865 + -4 x = 13.416407865 + -4 Combine like terms: 13.416407865 + -4 = 9.416407865 x = 9.416407865 Simplifying x = 9.416407865Subproblem 2
x + 4 = -13.416407865 Simplifying x + 4 = -13.416407865 Reorder the terms: 4 + x = -13.416407865 Solving 4 + x = -13.416407865 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 = -13.416407865 + -4 Combine like terms: 4 + -4 = 0 0 + x = -13.416407865 + -4 x = -13.416407865 + -4 Combine like terms: -13.416407865 + -4 = -17.416407865 x = -17.416407865 Simplifying x = -17.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.416407865, -17.416407865}
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