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Simplifying 144 = x2 + 16x Reorder the terms: 144 = 16x + x2 Solving 144 = 16x + x2 Solving for variable 'x'. Reorder the terms: 144 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 144 + -16x + -1x2 = 0 + x2 + -1x2 144 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 16x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 16x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 16x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 16x + x2 = 0 + 144 16x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 16x + x2 = 144 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 = 144 + 64 Reorder the terms: 64 + 16x + x2 = 144 + 64 Combine like terms: 144 + 64 = 208 64 + 16x + x2 = 208 Factor a perfect square on the left side: (x + 8)(x + 8) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + 8) equal to 14.422205102 and -14.422205102.Subproblem 1
x + 8 = 14.422205102 Simplifying x + 8 = 14.422205102 Reorder the terms: 8 + x = 14.422205102 Solving 8 + x = 14.422205102 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 = 14.422205102 + -8 Combine like terms: 8 + -8 = 0 0 + x = 14.422205102 + -8 x = 14.422205102 + -8 Combine like terms: 14.422205102 + -8 = 6.422205102 x = 6.422205102 Simplifying x = 6.422205102Subproblem 2
x + 8 = -14.422205102 Simplifying x + 8 = -14.422205102 Reorder the terms: 8 + x = -14.422205102 Solving 8 + x = -14.422205102 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 = -14.422205102 + -8 Combine like terms: 8 + -8 = 0 0 + x = -14.422205102 + -8 x = -14.422205102 + -8 Combine like terms: -14.422205102 + -8 = -22.422205102 x = -22.422205102 Simplifying x = -22.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.422205102, -22.422205102}
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