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Simplifying x2 + 32x + 144 = 0 Reorder the terms: 144 + 32x + x2 = 0 Solving 144 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + 32x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + 32x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + 32x + x2 = 0 + -144 32x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 32x + x2 = -144 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -144 + 256 Reorder the terms: 256 + 32x + x2 = -144 + 256 Combine like terms: -144 + 256 = 112 256 + 32x + x2 = 112 Factor a perfect square on the left side: (x + 16)(x + 16) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (x + 16) equal to 10.583005244 and -10.583005244.Subproblem 1
x + 16 = 10.583005244 Simplifying x + 16 = 10.583005244 Reorder the terms: 16 + x = 10.583005244 Solving 16 + x = 10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 10.583005244 + -16 Combine like terms: 16 + -16 = 0 0 + x = 10.583005244 + -16 x = 10.583005244 + -16 Combine like terms: 10.583005244 + -16 = -5.416994756 x = -5.416994756 Simplifying x = -5.416994756Subproblem 2
x + 16 = -10.583005244 Simplifying x + 16 = -10.583005244 Reorder the terms: 16 + x = -10.583005244 Solving 16 + x = -10.583005244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -10.583005244 + -16 Combine like terms: 16 + -16 = 0 0 + x = -10.583005244 + -16 x = -10.583005244 + -16 Combine like terms: -10.583005244 + -16 = -26.583005244 x = -26.583005244 Simplifying x = -26.583005244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.416994756, -26.583005244}
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