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Simplifying 2x2 + 26x + -480 = 0 Reorder the terms: -480 + 26x + 2x2 = 0 Solving -480 + 26x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-240 + 13x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-240 + 13x + x2)' equal to zero and attempt to solve: Simplifying -240 + 13x + x2 = 0 Solving -240 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 13x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 13x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 13x + x2 = 0 + 240 13x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 13x + x2 = 240 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 240 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 240 + 42.25 Combine like terms: 240 + 42.25 = 282.25 42.25 + 13x + x2 = 282.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (x + 6.5) equal to 16.800297616 and -16.800297616.Subproblem 1
x + 6.5 = 16.800297616 Simplifying x + 6.5 = 16.800297616 Reorder the terms: 6.5 + x = 16.800297616 Solving 6.5 + x = 16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 16.800297616 + -6.5 x = 16.800297616 + -6.5 Combine like terms: 16.800297616 + -6.5 = 10.300297616 x = 10.300297616 Simplifying x = 10.300297616Subproblem 2
x + 6.5 = -16.800297616 Simplifying x + 6.5 = -16.800297616 Reorder the terms: 6.5 + x = -16.800297616 Solving 6.5 + x = -16.800297616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -16.800297616 + -6.5 x = -16.800297616 + -6.5 Combine like terms: -16.800297616 + -6.5 = -23.300297616 x = -23.300297616 Simplifying x = -23.300297616Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.300297616, -23.300297616}Solution
x = {10.300297616, -23.300297616}
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