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Simplifying -6x3 + 5x2 + 5x = 0 Reorder the terms: 5x + 5x2 + -6x3 = 0 Solving 5x + 5x2 + -6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 5x + -6x2) = 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 '(5 + 5x + -6x2)' equal to zero and attempt to solve: Simplifying 5 + 5x + -6x2 = 0 Solving 5 + 5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.8333333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.8333333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + 0.8333333333 -0.8333333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.8333333333x + x2 = 0.8333333333 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 0.8333333333 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 0.8333333333 + 0.1736111111 Combine like terms: 0.8333333333 + 0.1736111111 = 1.0069444444 0.1736111111 + -0.8333333333x + x2 = 1.0069444444 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 1.0069444444 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 1.003466215 and -1.003466215.Subproblem 1
x + -0.4166666667 = 1.003466215 Simplifying x + -0.4166666667 = 1.003466215 Reorder the terms: -0.4166666667 + x = 1.003466215 Solving -0.4166666667 + x = 1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 1.003466215 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 1.003466215 + 0.4166666667 x = 1.003466215 + 0.4166666667 Combine like terms: 1.003466215 + 0.4166666667 = 1.4201328817 x = 1.4201328817 Simplifying x = 1.4201328817Subproblem 2
x + -0.4166666667 = -1.003466215 Simplifying x + -0.4166666667 = -1.003466215 Reorder the terms: -0.4166666667 + x = -1.003466215 Solving -0.4166666667 + x = -1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -1.003466215 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -1.003466215 + 0.4166666667 x = -1.003466215 + 0.4166666667 Combine like terms: -1.003466215 + 0.4166666667 = -0.5867995483 x = -0.5867995483 Simplifying x = -0.5867995483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4201328817, -0.5867995483}Solution
x = {0, 1.4201328817, -0.5867995483}
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