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Simplifying 6x4 + -10x3 + -6x2 = 0 Reorder the terms: -6x2 + -10x3 + 6x4 = 0 Solving -6x2 + -10x3 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-3 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 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 '(-3 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + -5x + 3x2 = 0 Solving -3 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.666666667x + x2 = 0 + 1 -1.666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.666666667x + x2 = 1 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1 + 0.6944444447 Combine like terms: 1 + 0.6944444447 = 1.6944444447 0.6944444447 + -1.666666667x + x2 = 1.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.6944444447 Calculate the square root of the right side: 1.301708279 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.301708279 and -1.301708279.Subproblem 1
x + -0.8333333335 = 1.301708279 Simplifying x + -0.8333333335 = 1.301708279 Reorder the terms: -0.8333333335 + x = 1.301708279 Solving -0.8333333335 + x = 1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.301708279 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.301708279 + 0.8333333335 x = 1.301708279 + 0.8333333335 Combine like terms: 1.301708279 + 0.8333333335 = 2.1350416125 x = 2.1350416125 Simplifying x = 2.1350416125Subproblem 2
x + -0.8333333335 = -1.301708279 Simplifying x + -0.8333333335 = -1.301708279 Reorder the terms: -0.8333333335 + x = -1.301708279 Solving -0.8333333335 + x = -1.301708279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.301708279 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.301708279 + 0.8333333335 x = -1.301708279 + 0.8333333335 Combine like terms: -1.301708279 + 0.8333333335 = -0.4683749455 x = -0.4683749455 Simplifying x = -0.4683749455Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1350416125, -0.4683749455}Solution
x = {0, 2.1350416125, -0.4683749455}
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