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Simplifying 5x3 + 4x2 + -6x = 0 Reorder the terms: -6x + 4x2 + 5x3 = 0 Solving -6x + 4x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 4x + 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 '(-6 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + 5x2 = 0 Solving -6 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.8x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.8x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.8x + x2 = 0 + 1.2 0.8x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.8x + x2 = 1.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 1.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 1.2 + 0.16 Combine like terms: 1.2 + 0.16 = 1.36 0.16 + 0.8x + x2 = 1.36 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (x + 0.4) equal to 1.166190379 and -1.166190379.Subproblem 1
x + 0.4 = 1.166190379 Simplifying x + 0.4 = 1.166190379 Reorder the terms: 0.4 + x = 1.166190379 Solving 0.4 + x = 1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.166190379 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.166190379 + -0.4 x = 1.166190379 + -0.4 Combine like terms: 1.166190379 + -0.4 = 0.766190379 x = 0.766190379 Simplifying x = 0.766190379Subproblem 2
x + 0.4 = -1.166190379 Simplifying x + 0.4 = -1.166190379 Reorder the terms: 0.4 + x = -1.166190379 Solving 0.4 + x = -1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.166190379 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.166190379 + -0.4 x = -1.166190379 + -0.4 Combine like terms: -1.166190379 + -0.4 = -1.566190379 x = -1.566190379 Simplifying x = -1.566190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.766190379, -1.566190379}Solution
x = {0, 0.766190379, -1.566190379}
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