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Simplifying x2 + 8x + -152 = 0 Reorder the terms: -152 + 8x + x2 = 0 Solving -152 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '152' to each side of the equation. -152 + 8x + 152 + x2 = 0 + 152 Reorder the terms: -152 + 152 + 8x + x2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + 8x + x2 = 0 + 152 8x + x2 = 0 + 152 Combine like terms: 0 + 152 = 152 8x + x2 = 152 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 = 152 + 16 Reorder the terms: 16 + 8x + x2 = 152 + 16 Combine like terms: 152 + 16 = 168 16 + 8x + x2 = 168 Factor a perfect square on the left side: (x + 4)(x + 4) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + 4) equal to 12.961481397 and -12.961481397.Subproblem 1
x + 4 = 12.961481397 Simplifying x + 4 = 12.961481397 Reorder the terms: 4 + x = 12.961481397 Solving 4 + x = 12.961481397 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 = 12.961481397 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12.961481397 + -4 x = 12.961481397 + -4 Combine like terms: 12.961481397 + -4 = 8.961481397 x = 8.961481397 Simplifying x = 8.961481397Subproblem 2
x + 4 = -12.961481397 Simplifying x + 4 = -12.961481397 Reorder the terms: 4 + x = -12.961481397 Solving 4 + x = -12.961481397 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 = -12.961481397 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12.961481397 + -4 x = -12.961481397 + -4 Combine like terms: -12.961481397 + -4 = -16.961481397 x = -16.961481397 Simplifying x = -16.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.961481397, -16.961481397}
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