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Simplifying 5x2 + 80x + -280 = 0 Reorder the terms: -280 + 80x + 5x2 = 0 Solving -280 + 80x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-56 + 16x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-56 + 16x + x2)' equal to zero and attempt to solve: Simplifying -56 + 16x + x2 = 0 Solving -56 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 16x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 16x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 16x + x2 = 0 + 56 16x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 16x + x2 = 56 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 56 + 64 Reorder the terms: 64 + 16x + x2 = 56 + 64 Combine like terms: 56 + 64 = 120 64 + 16x + x2 = 120 Factor a perfect square on the left side: (x + 8)(x + 8) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + 8) equal to 10.95445115 and -10.95445115.Subproblem 1
x + 8 = 10.95445115 Simplifying x + 8 = 10.95445115 Reorder the terms: 8 + x = 10.95445115 Solving 8 + x = 10.95445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.95445115 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.95445115 + -8 x = 10.95445115 + -8 Combine like terms: 10.95445115 + -8 = 2.95445115 x = 2.95445115 Simplifying x = 2.95445115Subproblem 2
x + 8 = -10.95445115 Simplifying x + 8 = -10.95445115 Reorder the terms: 8 + x = -10.95445115 Solving 8 + x = -10.95445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.95445115 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.95445115 + -8 x = -10.95445115 + -8 Combine like terms: -10.95445115 + -8 = -18.95445115 x = -18.95445115 Simplifying x = -18.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.95445115, -18.95445115}Solution
x = {2.95445115, -18.95445115}
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