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Simplifying (X + -4)(X + -12) = 80 Reorder the terms: (-4 + X)(X + -12) = 80 Reorder the terms: (-4 + X)(-12 + X) = 80 Multiply (-4 + X) * (-12 + X) (-4(-12 + X) + X(-12 + X)) = 80 ((-12 * -4 + X * -4) + X(-12 + X)) = 80 ((48 + -4X) + X(-12 + X)) = 80 (48 + -4X + (-12 * X + X * X)) = 80 (48 + -4X + (-12X + X2)) = 80 Combine like terms: -4X + -12X = -16X (48 + -16X + X2) = 80 Solving 48 + -16X + X2 = 80 Solving for variable 'X'. Reorder the terms: 48 + -80 + -16X + X2 = 80 + -80 Combine like terms: 48 + -80 = -32 -32 + -16X + X2 = 80 + -80 Combine like terms: 80 + -80 = 0 -32 + -16X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -16X + 32 + X2 = 0 + 32 Reorder the terms: -32 + 32 + -16X + X2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -16X + X2 = 0 + 32 -16X + X2 = 0 + 32 Combine like terms: 0 + 32 = 32 -16X + X2 = 32 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 = 32 + 64 Reorder the terms: 64 + -16X + X2 = 32 + 64 Combine like terms: 32 + 64 = 96 64 + -16X + X2 = 96 Factor a perfect square on the left side: (X + -8)(X + -8) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (X + -8) equal to 9.797958971 and -9.797958971.Subproblem 1
X + -8 = 9.797958971 Simplifying X + -8 = 9.797958971 Reorder the terms: -8 + X = 9.797958971 Solving -8 + X = 9.797958971 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 = 9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + X = 9.797958971 + 8 X = 9.797958971 + 8 Combine like terms: 9.797958971 + 8 = 17.797958971 X = 17.797958971 Simplifying X = 17.797958971Subproblem 2
X + -8 = -9.797958971 Simplifying X + -8 = -9.797958971 Reorder the terms: -8 + X = -9.797958971 Solving -8 + X = -9.797958971 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 = -9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + X = -9.797958971 + 8 X = -9.797958971 + 8 Combine like terms: -9.797958971 + 8 = -1.797958971 X = -1.797958971 Simplifying X = -1.797958971Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.797958971, -1.797958971}
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