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Simplifying 8x2 + 68x + -280 = 0 Reorder the terms: -280 + 68x + 8x2 = 0 Solving -280 + 68x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-70 + 17x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-70 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying -70 + 17x + 2x2 = 0 Solving -70 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -35 + 8.5x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 8.5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 8.5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 8.5x + x2 = 0 + 35 8.5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 8.5x + x2 = 35 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 35 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 35 + 18.0625 Combine like terms: 35 + 18.0625 = 53.0625 18.0625 + 8.5x + x2 = 53.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 53.0625 Calculate the square root of the right side: 7.284401142 Break this problem into two subproblems by setting (x + 4.25) equal to 7.284401142 and -7.284401142.Subproblem 1
x + 4.25 = 7.284401142 Simplifying x + 4.25 = 7.284401142 Reorder the terms: 4.25 + x = 7.284401142 Solving 4.25 + x = 7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 7.284401142 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 7.284401142 + -4.25 x = 7.284401142 + -4.25 Combine like terms: 7.284401142 + -4.25 = 3.034401142 x = 3.034401142 Simplifying x = 3.034401142Subproblem 2
x + 4.25 = -7.284401142 Simplifying x + 4.25 = -7.284401142 Reorder the terms: 4.25 + x = -7.284401142 Solving 4.25 + x = -7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -7.284401142 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -7.284401142 + -4.25 x = -7.284401142 + -4.25 Combine like terms: -7.284401142 + -4.25 = -11.534401142 x = -11.534401142 Simplifying x = -11.534401142Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.034401142, -11.534401142}Solution
x = {3.034401142, -11.534401142}
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