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Simplifying 5x4 + -7x3 + -2x2 = 0 Reorder the terms: -2x2 + -7x3 + 5x4 = 0 Solving -2x2 + -7x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-2 + -7x + 5x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-2 + -7x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + -7x + 5x2 = 0 Solving -2 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -1.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.4x + x2 = 0 + 0.4 -1.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -1.4x + x2 = 0.4 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.4 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + -1.4x + x2 = 0.89 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -0.7 = 0.943398113 Simplifying x + -0.7 = 0.943398113 Reorder the terms: -0.7 + x = 0.943398113 Solving -0.7 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.943398113 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.943398113 + 0.7 x = 0.943398113 + 0.7 Combine like terms: 0.943398113 + 0.7 = 1.643398113 x = 1.643398113 Simplifying x = 1.643398113Subproblem 2
x + -0.7 = -0.943398113 Simplifying x + -0.7 = -0.943398113 Reorder the terms: -0.7 + x = -0.943398113 Solving -0.7 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.943398113 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.943398113 + 0.7 x = -0.943398113 + 0.7 Combine like terms: -0.943398113 + 0.7 = -0.243398113 x = -0.243398113 Simplifying x = -0.243398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.643398113, -0.243398113}Solution
x = {0, 1.643398113, -0.243398113}
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