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Simplifying x2 + 8x + 100 = 180 Reorder the terms: 100 + 8x + x2 = 180 Solving 100 + 8x + x2 = 180 Solving for variable 'x'. Reorder the terms: 100 + -180 + 8x + x2 = 180 + -180 Combine like terms: 100 + -180 = -80 -80 + 8x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -80 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 8x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 8x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 8x + x2 = 0 + 80 8x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 8x + x2 = 80 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 = 80 + 16 Reorder the terms: 16 + 8x + x2 = 80 + 16 Combine like terms: 80 + 16 = 96 16 + 8x + x2 = 96 Factor a perfect square on the left side: (x + 4)(x + 4) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 4) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 4 = 9.797958971 Simplifying x + 4 = 9.797958971 Reorder the terms: 4 + x = 9.797958971 Solving 4 + x = 9.797958971 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 = 9.797958971 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.797958971 + -4 x = 9.797958971 + -4 Combine like terms: 9.797958971 + -4 = 5.797958971 x = 5.797958971 Simplifying x = 5.797958971Subproblem 2
x + 4 = -9.797958971 Simplifying x + 4 = -9.797958971 Reorder the terms: 4 + x = -9.797958971 Solving 4 + x = -9.797958971 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 = -9.797958971 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.797958971 + -4 x = -9.797958971 + -4 Combine like terms: -9.797958971 + -4 = -13.797958971 x = -13.797958971 Simplifying x = -13.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.797958971, -13.797958971}
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