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Simplifying 16x + 120 = x2 Reorder the terms: 120 + 16x = x2 Solving 120 + 16x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 120 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + -16x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -16x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -16x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -16x + x2 = 0 + 120 -16x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -16x + x2 = 120 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 = 120 + 64 Reorder the terms: 64 + -16x + x2 = 120 + 64 Combine like terms: 120 + 64 = 184 64 + -16x + x2 = 184 Factor a perfect square on the left side: (x + -8)(x + -8) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + -8) equal to 13.564659966 and -13.564659966.Subproblem 1
x + -8 = 13.564659966 Simplifying x + -8 = 13.564659966 Reorder the terms: -8 + x = 13.564659966 Solving -8 + x = 13.564659966 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 = 13.564659966 + 8 Combine like terms: -8 + 8 = 0 0 + x = 13.564659966 + 8 x = 13.564659966 + 8 Combine like terms: 13.564659966 + 8 = 21.564659966 x = 21.564659966 Simplifying x = 21.564659966Subproblem 2
x + -8 = -13.564659966 Simplifying x + -8 = -13.564659966 Reorder the terms: -8 + x = -13.564659966 Solving -8 + x = -13.564659966 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 = -13.564659966 + 8 Combine like terms: -8 + 8 = 0 0 + x = -13.564659966 + 8 x = -13.564659966 + 8 Combine like terms: -13.564659966 + 8 = -5.564659966 x = -5.564659966 Simplifying x = -5.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.564659966, -5.564659966}
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