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Simplifying 5x3 + 3x2 = 4x Reorder the terms: 3x2 + 5x3 = 4x Solving 3x2 + 5x3 = 4x Solving for variable 'x'. Reorder the terms: -4x + 3x2 + 5x3 = 4x + -4x Combine like terms: 4x + -4x = 0 -4x + 3x2 + 5x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 3x + 5x2) = 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 '(-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 = 0.643398113 x = 0.643398113 Simplifying x = 0.643398113Subproblem 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 = -1.243398113 x = -1.243398113 Simplifying x = -1.243398113Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.643398113, -1.243398113}Solution
x = {0, 0.643398113, -1.243398113}
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