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Simplifying 8x2 + -4x + -90 = 0 Reorder the terms: -90 + -4x + 8x2 = 0 Solving -90 + -4x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -2x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -2x + 4x2)' equal to zero and attempt to solve: Simplifying -45 + -2x + 4x2 = 0 Solving -45 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -0.5x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -0.5x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -0.5x + x2 = 0 + 11.25 -0.5x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -0.5x + x2 = 11.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 11.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 11.25 + 0.0625 Combine like terms: 11.25 + 0.0625 = 11.3125 0.0625 + -0.5x + x2 = 11.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 11.3125 Calculate the square root of the right side: 3.363406012 Break this problem into two subproblems by setting (x + -0.25) equal to 3.363406012 and -3.363406012.Subproblem 1
x + -0.25 = 3.363406012 Simplifying x + -0.25 = 3.363406012 Reorder the terms: -0.25 + x = 3.363406012 Solving -0.25 + x = 3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 3.363406012 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.363406012 + 0.25 x = 3.363406012 + 0.25 Combine like terms: 3.363406012 + 0.25 = 3.613406012 x = 3.613406012 Simplifying x = 3.613406012Subproblem 2
x + -0.25 = -3.363406012 Simplifying x + -0.25 = -3.363406012 Reorder the terms: -0.25 + x = -3.363406012 Solving -0.25 + x = -3.363406012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -3.363406012 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.363406012 + 0.25 x = -3.363406012 + 0.25 Combine like terms: -3.363406012 + 0.25 = -3.113406012 x = -3.113406012 Simplifying x = -3.113406012Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.613406012, -3.113406012}Solution
x = {3.613406012, -3.113406012}
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