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Simplifying 80 = (16 + -1x)(8 + -1x) Multiply (16 + -1x) * (8 + -1x) 80 = (16(8 + -1x) + -1x * (8 + -1x)) 80 = ((8 * 16 + -1x * 16) + -1x * (8 + -1x)) 80 = ((128 + -16x) + -1x * (8 + -1x)) 80 = (128 + -16x + (8 * -1x + -1x * -1x)) 80 = (128 + -16x + (-8x + 1x2)) Combine like terms: -16x + -8x = -24x 80 = (128 + -24x + 1x2) Solving 80 = 128 + -24x + 1x2 Solving for variable 'x'. Combine like terms: 80 + -128 = -48 -48 + 24x + -1x2 = 128 + -24x + 1x2 + -128 + 24x + -1x2 Reorder the terms: -48 + 24x + -1x2 = 128 + -128 + -24x + 24x + 1x2 + -1x2 Combine like terms: 128 + -128 = 0 -48 + 24x + -1x2 = 0 + -24x + 24x + 1x2 + -1x2 -48 + 24x + -1x2 = -24x + 24x + 1x2 + -1x2 Combine like terms: -24x + 24x = 0 -48 + 24x + -1x2 = 0 + 1x2 + -1x2 -48 + 24x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -48 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 48 + -24x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + -24x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -24x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -24x + x2 = 0 + -48 -24x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -24x + x2 = -48 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -48 + 144 Reorder the terms: 144 + -24x + x2 = -48 + 144 Combine like terms: -48 + 144 = 96 144 + -24x + x2 = 96 Factor a perfect square on the left side: (x + -12)(x + -12) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -12) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -12 = 9.797958971 Simplifying x + -12 = 9.797958971 Reorder the terms: -12 + x = 9.797958971 Solving -12 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 9.797958971 + 12 Combine like terms: -12 + 12 = 0 0 + x = 9.797958971 + 12 x = 9.797958971 + 12 Combine like terms: 9.797958971 + 12 = 21.797958971 x = 21.797958971 Simplifying x = 21.797958971Subproblem 2
x + -12 = -9.797958971 Simplifying x + -12 = -9.797958971 Reorder the terms: -12 + x = -9.797958971 Solving -12 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -9.797958971 + 12 Combine like terms: -12 + 12 = 0 0 + x = -9.797958971 + 12 x = -9.797958971 + 12 Combine like terms: -9.797958971 + 12 = 2.202041029 x = 2.202041029 Simplifying x = 2.202041029Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.797958971, 2.202041029}
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