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Simplifying 6x3 + -9x2 + 1x = 0 Reorder the terms: 1x + -9x2 + 6x3 = 0 Solving 1x + -9x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -9x + 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 '(1 + -9x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + -9x + 6x2 = 0 Solving 1 + -9x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -1.5x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -1.5x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + -0.1666666667 -1.5x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -1.5x + x2 = -0.1666666667 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.1666666667 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.1666666667 + 0.5625 Combine like terms: -0.1666666667 + 0.5625 = 0.3958333333 0.5625 + -1.5x + x2 = 0.3958333333 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (x + -0.75) equal to 0.62915287 and -0.62915287.Subproblem 1
x + -0.75 = 0.62915287 Simplifying x + -0.75 = 0.62915287 Reorder the terms: -0.75 + x = 0.62915287 Solving -0.75 + x = 0.62915287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.62915287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.62915287 + 0.75 x = 0.62915287 + 0.75 Combine like terms: 0.62915287 + 0.75 = 1.37915287 x = 1.37915287 Simplifying x = 1.37915287Subproblem 2
x + -0.75 = -0.62915287 Simplifying x + -0.75 = -0.62915287 Reorder the terms: -0.75 + x = -0.62915287 Solving -0.75 + x = -0.62915287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.62915287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.62915287 + 0.75 x = -0.62915287 + 0.75 Combine like terms: -0.62915287 + 0.75 = 0.12084713 x = 0.12084713 Simplifying x = 0.12084713Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.37915287, 0.12084713}Solution
x = {0, 1.37915287, 0.12084713}
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