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Simplifying 14x2 + 26x + -160 = 0 Reorder the terms: -160 + 26x + 14x2 = 0 Solving -160 + 26x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + 13x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + 13x + 7x2)' equal to zero and attempt to solve: Simplifying -80 + 13x + 7x2 = 0 Solving -80 + 13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -11.42857143 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '11.42857143' to each side of the equation. -11.42857143 + 1.857142857x + 11.42857143 + x2 = 0 + 11.42857143 Reorder the terms: -11.42857143 + 11.42857143 + 1.857142857x + x2 = 0 + 11.42857143 Combine like terms: -11.42857143 + 11.42857143 = 0.00000000 0.00000000 + 1.857142857x + x2 = 0 + 11.42857143 1.857142857x + x2 = 0 + 11.42857143 Combine like terms: 0 + 11.42857143 = 11.42857143 1.857142857x + x2 = 11.42857143 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = 11.42857143 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 11.42857143 + 0.8622448978 Combine like terms: 11.42857143 + 0.8622448978 = 12.2908163278 0.8622448978 + 1.857142857x + x2 = 12.2908163278 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 12.2908163278 Calculate the square root of the right side: 3.505826055 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 3.505826055 and -3.505826055.Subproblem 1
x + 0.9285714285 = 3.505826055 Simplifying x + 0.9285714285 = 3.505826055 Reorder the terms: 0.9285714285 + x = 3.505826055 Solving 0.9285714285 + x = 3.505826055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 3.505826055 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 3.505826055 + -0.9285714285 x = 3.505826055 + -0.9285714285 Combine like terms: 3.505826055 + -0.9285714285 = 2.5772546265 x = 2.5772546265 Simplifying x = 2.5772546265Subproblem 2
x + 0.9285714285 = -3.505826055 Simplifying x + 0.9285714285 = -3.505826055 Reorder the terms: 0.9285714285 + x = -3.505826055 Solving 0.9285714285 + x = -3.505826055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -3.505826055 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -3.505826055 + -0.9285714285 x = -3.505826055 + -0.9285714285 Combine like terms: -3.505826055 + -0.9285714285 = -4.4343974835 x = -4.4343974835 Simplifying x = -4.4343974835Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5772546265, -4.4343974835}Solution
x = {2.5772546265, -4.4343974835}
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