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Simplifying 6x4 + 21x3 + -18x2 = 0 Reorder the terms: -18x2 + 21x3 + 6x4 = 0 Solving -18x2 + 21x3 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-6 + 7x + 2x2) = 0 Ignore the factor 3.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 '(-6 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + 7x + 2x2 = 0 Solving -6 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 3.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.5x + x2 = 0 + 3 3.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.5x + x2 = 3 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 3 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + 3.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 1.75 = 2.46221445 Simplifying x + 1.75 = 2.46221445 Reorder the terms: 1.75 + x = 2.46221445 Solving 1.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.46221445 + -1.75 x = 2.46221445 + -1.75 Combine like terms: 2.46221445 + -1.75 = 0.71221445 x = 0.71221445 Simplifying x = 0.71221445Subproblem 2
x + 1.75 = -2.46221445 Simplifying x + 1.75 = -2.46221445 Reorder the terms: 1.75 + x = -2.46221445 Solving 1.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.46221445 + -1.75 x = -2.46221445 + -1.75 Combine like terms: -2.46221445 + -1.75 = -4.21221445 x = -4.21221445 Simplifying x = -4.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71221445, -4.21221445}Solution
x = {0, 0.71221445, -4.21221445}
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