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Simplifying 8x2 + -16x + -80 = 8 Reorder the terms: -80 + -16x + 8x2 = 8 Solving -80 + -16x + 8x2 = 8 Solving for variable 'x'. Reorder the terms: -80 + -8 + -16x + 8x2 = 8 + -8 Combine like terms: -80 + -8 = -88 -88 + -16x + 8x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -88 + -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-11 + -2x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-11 + -2x + x2)' equal to zero and attempt to solve: Simplifying -11 + -2x + x2 = 0 Solving -11 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -2x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -2x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2x + x2 = 0 + 11 -2x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2x + x2 = 11 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 11 + 1 Reorder the terms: 1 + -2x + x2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2x + x2 = 12 Factor a perfect square on the left side: (x + -1)(x + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -1 = 3.464101615 Simplifying x + -1 = 3.464101615 Reorder the terms: -1 + x = 3.464101615 Solving -1 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.464101615 + 1 x = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 x = 4.464101615 Simplifying x = 4.464101615Subproblem 2
x + -1 = -3.464101615 Simplifying x + -1 = -3.464101615 Reorder the terms: -1 + x = -3.464101615 Solving -1 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.464101615 + 1 x = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 x = -2.464101615 Simplifying x = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.464101615, -2.464101615}Solution
x = {4.464101615, -2.464101615}
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