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Simplifying 180 = x2 + 16x + 131 Reorder the terms: 180 = 131 + 16x + x2 Solving 180 = 131 + 16x + x2 Solving for variable 'x'. Combine like terms: 180 + -131 = 49 49 + -16x + -1x2 = 131 + 16x + x2 + -131 + -16x + -1x2 Reorder the terms: 49 + -16x + -1x2 = 131 + -131 + 16x + -16x + x2 + -1x2 Combine like terms: 131 + -131 = 0 49 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 49 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 49 + -16x + -1x2 = 0 + x2 + -1x2 49 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 49 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 16x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 16x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 16x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 16x + x2 = 0 + 49 16x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 16x + x2 = 49 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 49 + 64 Reorder the terms: 64 + 16x + x2 = 49 + 64 Combine like terms: 49 + 64 = 113 64 + 16x + x2 = 113 Factor a perfect square on the left side: (x + 8)(x + 8) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 8) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 8 = 10.630145813 Simplifying x + 8 = 10.630145813 Reorder the terms: 8 + x = 10.630145813 Solving 8 + x = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.630145813 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.630145813 + -8 x = 10.630145813 + -8 Combine like terms: 10.630145813 + -8 = 2.630145813 x = 2.630145813 Simplifying x = 2.630145813Subproblem 2
x + 8 = -10.630145813 Simplifying x + 8 = -10.630145813 Reorder the terms: 8 + x = -10.630145813 Solving 8 + x = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.630145813 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.630145813 + -8 x = -10.630145813 + -8 Combine like terms: -10.630145813 + -8 = -18.630145813 x = -18.630145813 Simplifying x = -18.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.630145813, -18.630145813}
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