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Simplifying 26x2 + 14x3 = 2x Solving 26x2 + 14x3 = 2x Solving for variable 'x'. Reorder the terms: -2x + 26x2 + 14x3 = 2x + -2x Combine like terms: 2x + -2x = 0 -2x + 26x2 + 14x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 13x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + 13x + 7x2)' equal to zero and attempt to solve: Simplifying -1 + 13x + 7x2 = 0 Solving -1 + 13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 1.857142857x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 1.857142857x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 1.857142857x + x2 = 0 + 0.1428571429 1.857142857x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 1.857142857x + x2 = 0.1428571429 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 = 0.1428571429 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 0.1428571429 + 0.8622448978 Combine like terms: 0.1428571429 + 0.8622448978 = 1.0051020407 0.8622448978 + 1.857142857x + x2 = 1.0051020407 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 1.0051020407 Calculate the square root of the right side: 1.002547775 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 1.002547775 and -1.002547775.Subproblem 1
x + 0.9285714285 = 1.002547775 Simplifying x + 0.9285714285 = 1.002547775 Reorder the terms: 0.9285714285 + x = 1.002547775 Solving 0.9285714285 + x = 1.002547775 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 = 1.002547775 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 1.002547775 + -0.9285714285 x = 1.002547775 + -0.9285714285 Combine like terms: 1.002547775 + -0.9285714285 = 0.0739763465 x = 0.0739763465 Simplifying x = 0.0739763465Subproblem 2
x + 0.9285714285 = -1.002547775 Simplifying x + 0.9285714285 = -1.002547775 Reorder the terms: 0.9285714285 + x = -1.002547775 Solving 0.9285714285 + x = -1.002547775 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 = -1.002547775 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -1.002547775 + -0.9285714285 x = -1.002547775 + -0.9285714285 Combine like terms: -1.002547775 + -0.9285714285 = -1.9311192035 x = -1.9311192035 Simplifying x = -1.9311192035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0739763465, -1.9311192035}Solution
x = {0, 0.0739763465, -1.9311192035}
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