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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 = 5.681145748 x = 5.681145748 Simplifying x = 5.681145748Subproblem 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 = -9.681145748 x = -9.681145748 Simplifying x = -9.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.681145748, -9.681145748}Solution
x = {5.681145748, -9.681145748}
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