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Simplifying 7x2 + 151x + -1372 = 0 Reorder the terms: -1372 + 151x + 7x2 = 0 Solving -1372 + 151x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -196 + 21.57142857x + x2 = 0 Move the constant term to the right: Add '196' to each side of the equation. -196 + 21.57142857x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + 21.57142857x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 21.57142857x + x2 = 0 + 196 21.57142857x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 21.57142857x + x2 = 196 The x term is 21.57142857x. Take half its coefficient (10.78571429). Square it (116.3316327) and add it to both sides. Add '116.3316327' to each side of the equation. 21.57142857x + 116.3316327 + x2 = 196 + 116.3316327 Reorder the terms: 116.3316327 + 21.57142857x + x2 = 196 + 116.3316327 Combine like terms: 196 + 116.3316327 = 312.3316327 116.3316327 + 21.57142857x + x2 = 312.3316327 Factor a perfect square on the left side: (x + 10.78571429)(x + 10.78571429) = 312.3316327 Calculate the square root of the right side: 17.672906742 Break this problem into two subproblems by setting (x + 10.78571429) equal to 17.672906742 and -17.672906742.Subproblem 1
x + 10.78571429 = 17.672906742 Simplifying x + 10.78571429 = 17.672906742 Reorder the terms: 10.78571429 + x = 17.672906742 Solving 10.78571429 + x = 17.672906742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.78571429' to each side of the equation. 10.78571429 + -10.78571429 + x = 17.672906742 + -10.78571429 Combine like terms: 10.78571429 + -10.78571429 = 0.00000000 0.00000000 + x = 17.672906742 + -10.78571429 x = 17.672906742 + -10.78571429 Combine like terms: 17.672906742 + -10.78571429 = 6.887192452 x = 6.887192452 Simplifying x = 6.887192452Subproblem 2
x + 10.78571429 = -17.672906742 Simplifying x + 10.78571429 = -17.672906742 Reorder the terms: 10.78571429 + x = -17.672906742 Solving 10.78571429 + x = -17.672906742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.78571429' to each side of the equation. 10.78571429 + -10.78571429 + x = -17.672906742 + -10.78571429 Combine like terms: 10.78571429 + -10.78571429 = 0.00000000 0.00000000 + x = -17.672906742 + -10.78571429 x = -17.672906742 + -10.78571429 Combine like terms: -17.672906742 + -10.78571429 = -28.458621032 x = -28.458621032 Simplifying x = -28.458621032Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.887192452, -28.458621032}
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