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Simplifying 5x4 + -3x3 + -4x2 = 0 Reorder the terms: -4x2 + -3x3 + 5x4 = 0 Solving -4x2 + -3x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -3x + 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 '(-4 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -4 + -3x + 5x2 = 0 Solving -4 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.6x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.6x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.6x + x2 = 0 + 0.8 -0.6x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.6x + x2 = 0.8 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.8 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.8 + 0.09 Combine like terms: 0.8 + 0.09 = 0.89 0.09 + -0.6x + x2 = 0.89 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -0.3) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -0.3 = 0.943398113 Simplifying x + -0.3 = 0.943398113 Reorder the terms: -0.3 + x = 0.943398113 Solving -0.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.943398113 + 0.3 x = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 x = 1.243398113 Simplifying x = 1.243398113Subproblem 2
x + -0.3 = -0.943398113 Simplifying x + -0.3 = -0.943398113 Reorder the terms: -0.3 + x = -0.943398113 Solving -0.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.943398113 + 0.3 x = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 x = -0.643398113 Simplifying x = -0.643398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.243398113, -0.643398113}Solution
x = {0, 1.243398113, -0.643398113}
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