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Simplifying 8x2 + 8x + -42 = 0 Reorder the terms: -42 + 8x + 8x2 = 0 Solving -42 + 8x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 4x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying -21 + 4x + 4x2 = 0 Solving -21 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x + x2 = 0 + 5.25 x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 x + x2 = 5.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.25 + 0.25 Combine like terms: 5.25 + 0.25 = 5.5 1.25 + x2 = 5.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + 0.5) equal to 2.34520788 and -2.34520788.Subproblem 1
x + 0.5 = 2.34520788 Simplifying x + 0.5 = 2.34520788 Reorder the terms: 0.5 + x = 2.34520788 Solving 0.5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.34520788 + -0.5 x = 2.34520788 + -0.5 Combine like terms: 2.34520788 + -0.5 = 1.84520788 x = 1.84520788 Simplifying x = 1.84520788Subproblem 2
x + 0.5 = -2.34520788 Simplifying x + 0.5 = -2.34520788 Reorder the terms: 0.5 + x = -2.34520788 Solving 0.5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.34520788 + -0.5 x = -2.34520788 + -0.5 Combine like terms: -2.34520788 + -0.5 = -2.84520788 x = -2.84520788 Simplifying x = -2.84520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.84520788, -2.84520788}Solution
x = {1.84520788, -2.84520788}
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