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Simplifying (x + 5)(x + 5) = 180 Reorder the terms: (5 + x)(x + 5) = 180 Reorder the terms: (5 + x)(5 + x) = 180 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 180 ((5 * 5 + x * 5) + x(5 + x)) = 180 ((25 + 5x) + x(5 + x)) = 180 (25 + 5x + (5 * x + x * x)) = 180 (25 + 5x + (5x + x2)) = 180 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 180 Solving 25 + 10x + x2 = 180 Solving for variable 'x'. Reorder the terms: 25 + -180 + 10x + x2 = 180 + -180 Combine like terms: 25 + -180 = -155 -155 + 10x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -155 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + 10x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + 10x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + 10x + x2 = 0 + 155 10x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 10x + x2 = 155 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 155 + 25 Reorder the terms: 25 + 10x + x2 = 155 + 25 Combine like terms: 155 + 25 = 180 25 + 10x + x2 = 180 Factor a perfect square on the left side: (x + 5)(x + 5) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 5) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 5 = 13.416407865 Simplifying x + 5 = 13.416407865 Reorder the terms: 5 + x = 13.416407865 Solving 5 + x = 13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 13.416407865 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.416407865 + -5 x = 13.416407865 + -5 Combine like terms: 13.416407865 + -5 = 8.416407865 x = 8.416407865 Simplifying x = 8.416407865Subproblem 2
x + 5 = -13.416407865 Simplifying x + 5 = -13.416407865 Reorder the terms: 5 + x = -13.416407865 Solving 5 + x = -13.416407865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -13.416407865 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.416407865 + -5 x = -13.416407865 + -5 Combine like terms: -13.416407865 + -5 = -18.416407865 x = -18.416407865 Simplifying x = -18.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.416407865, -18.416407865}
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