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Simplifying 2x2 + -8x + -42 = 68 Reorder the terms: -42 + -8x + 2x2 = 68 Solving -42 + -8x + 2x2 = 68 Solving for variable 'x'. Reorder the terms: -42 + -68 + -8x + 2x2 = 68 + -68 Combine like terms: -42 + -68 = -110 -110 + -8x + 2x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -110 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + -4x + x2)' equal to zero and attempt to solve: Simplifying -55 + -4x + x2 = 0 Solving -55 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -4x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -4x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -4x + x2 = 0 + 55 -4x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -4x + x2 = 55 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 55 + 4 Reorder the terms: 4 + -4x + x2 = 55 + 4 Combine like terms: 55 + 4 = 59 4 + -4x + x2 = 59 Factor a perfect square on the left side: (x + -2)(x + -2) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + -2) equal to 7.681145748 and -7.681145748.Subproblem 1
x + -2 = 7.681145748 Simplifying x + -2 = 7.681145748 Reorder the terms: -2 + x = 7.681145748 Solving -2 + x = 7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.681145748 + 2 x = 7.681145748 + 2 Combine like terms: 7.681145748 + 2 = 9.681145748 x = 9.681145748 Simplifying x = 9.681145748Subproblem 2
x + -2 = -7.681145748 Simplifying x + -2 = -7.681145748 Reorder the terms: -2 + x = -7.681145748 Solving -2 + x = -7.681145748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.681145748 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.681145748 + 2 x = -7.681145748 + 2 Combine like terms: -7.681145748 + 2 = -5.681145748 x = -5.681145748 Simplifying x = -5.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.681145748, -5.681145748}Solution
x = {9.681145748, -5.681145748}
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