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Simplifying 7x3 + -13x2 + -7x = 0 Reorder the terms: -7x + -13x2 + 7x3 = 0 Solving -7x + -13x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + -13x + 7x2) = 0Subproblem 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 '(-7 + -13x + 7x2)' equal to zero and attempt to solve: Simplifying -7 + -13x + 7x2 = 0 Solving -7 + -13x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -1.857142857x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.857142857x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.857142857x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.857142857x + x2 = 0 + 1 -1.857142857x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.857142857x + x2 = 1 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 = 1 + 0.8622448978 Reorder the terms: 0.8622448978 + -1.857142857x + x2 = 1 + 0.8622448978 Combine like terms: 1 + 0.8622448978 = 1.8622448978 0.8622448978 + -1.857142857x + x2 = 1.8622448978 Factor a perfect square on the left side: (x + -0.9285714285)(x + -0.9285714285) = 1.8622448978 Calculate the square root of the right side: 1.364640941 Break this problem into two subproblems by setting (x + -0.9285714285) equal to 1.364640941 and -1.364640941.Subproblem 1
x + -0.9285714285 = 1.364640941 Simplifying x + -0.9285714285 = 1.364640941 Reorder the terms: -0.9285714285 + x = 1.364640941 Solving -0.9285714285 + x = 1.364640941 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 = 1.364640941 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.364640941 + 0.9285714285 x = 1.364640941 + 0.9285714285 Combine like terms: 1.364640941 + 0.9285714285 = 2.2932123695 x = 2.2932123695 Simplifying x = 2.2932123695Subproblem 2
x + -0.9285714285 = -1.364640941 Simplifying x + -0.9285714285 = -1.364640941 Reorder the terms: -0.9285714285 + x = -1.364640941 Solving -0.9285714285 + x = -1.364640941 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 = -1.364640941 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.364640941 + 0.9285714285 x = -1.364640941 + 0.9285714285 Combine like terms: -1.364640941 + 0.9285714285 = -0.4360695125 x = -0.4360695125 Simplifying x = -0.4360695125Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2932123695, -0.4360695125}Solution
x = {0, 2.2932123695, -0.4360695125}
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