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Simplifying 30x6 + -18x5 + -9x4 = 0 Reorder the terms: -9x4 + -18x5 + 30x6 = 0 Solving -9x4 + -18x5 + 30x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x4'. 3x4(-3 + -6x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + -6x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + -6x + 10x2 = 0 Solving -3 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.6x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.6x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.6x + x2 = 0.0 + 0.3 -0.6x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.6x + x2 = 0.3 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 = 0.3 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.3 + 0.09 Combine like terms: 0.3 + 0.09 = 0.39 0.09 + -0.6x + x2 = 0.39 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.39 Calculate the square root of the right side: 0.6244998 Break this problem into two subproblems by setting (x + -0.3) equal to 0.6244998 and -0.6244998.Subproblem 1
x + -0.3 = 0.6244998 Simplifying x + -0.3 = 0.6244998 Reorder the terms: -0.3 + x = 0.6244998 Solving -0.3 + x = 0.6244998 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 = 0.6244998 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.6244998 + 0.3 x = 0.6244998 + 0.3 Combine like terms: 0.6244998 + 0.3 = 0.9244998 x = 0.9244998 Simplifying x = 0.9244998Subproblem 2
x + -0.3 = -0.6244998 Simplifying x + -0.3 = -0.6244998 Reorder the terms: -0.3 + x = -0.6244998 Solving -0.3 + x = -0.6244998 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 = -0.6244998 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.6244998 + 0.3 x = -0.6244998 + 0.3 Combine like terms: -0.6244998 + 0.3 = -0.3244998 x = -0.3244998 Simplifying x = -0.3244998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9244998, -0.3244998}Solution
x = {0.9244998, -0.3244998}
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