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Simplifying 3x2 + 31x + -420 = 0 Reorder the terms: -420 + 31x + 3x2 = 0 Solving -420 + 31x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -140 + 10.33333333x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 10.33333333x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 10.33333333x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 10.33333333x + x2 = 0 + 140 10.33333333x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 10.33333333x + x2 = 140 The x term is 10.33333333x. Take half its coefficient (5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. 10.33333333x + 26.69444443 + x2 = 140 + 26.69444443 Reorder the terms: 26.69444443 + 10.33333333x + x2 = 140 + 26.69444443 Combine like terms: 140 + 26.69444443 = 166.69444443 26.69444443 + 10.33333333x + x2 = 166.69444443 Factor a perfect square on the left side: (x + 5.166666665)(x + 5.166666665) = 166.69444443 Calculate the square root of the right side: 12.911020271 Break this problem into two subproblems by setting (x + 5.166666665) equal to 12.911020271 and -12.911020271.Subproblem 1
x + 5.166666665 = 12.911020271 Simplifying x + 5.166666665 = 12.911020271 Reorder the terms: 5.166666665 + x = 12.911020271 Solving 5.166666665 + x = 12.911020271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = 12.911020271 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = 12.911020271 + -5.166666665 x = 12.911020271 + -5.166666665 Combine like terms: 12.911020271 + -5.166666665 = 7.744353606 x = 7.744353606 Simplifying x = 7.744353606Subproblem 2
x + 5.166666665 = -12.911020271 Simplifying x + 5.166666665 = -12.911020271 Reorder the terms: 5.166666665 + x = -12.911020271 Solving 5.166666665 + x = -12.911020271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = -12.911020271 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = -12.911020271 + -5.166666665 x = -12.911020271 + -5.166666665 Combine like terms: -12.911020271 + -5.166666665 = -18.077686936 x = -18.077686936 Simplifying x = -18.077686936Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.744353606, -18.077686936}
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