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Simplifying 2x4 + -5x3 + -9x2 = 0 Reorder the terms: -9x2 + -5x3 + 2x4 = 0 Solving -9x2 + -5x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-9 + -5x + 2x2) = 0Subproblem 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 '(-9 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -9 + -5x + 2x2 = 0 Solving -9 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -2.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -2.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -2.5x + x2 = 0 + 4.5 -2.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -2.5x + x2 = 4.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 4.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4.5 + 1.5625 Combine like terms: 4.5 + 1.5625 = 6.0625 1.5625 + -2.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -1.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -1.25 = 2.46221445 Simplifying x + -1.25 = 2.46221445 Reorder the terms: -1.25 + x = 2.46221445 Solving -1.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.46221445 + 1.25 x = 2.46221445 + 1.25 Combine like terms: 2.46221445 + 1.25 = 3.71221445 x = 3.71221445 Simplifying x = 3.71221445Subproblem 2
x + -1.25 = -2.46221445 Simplifying x + -1.25 = -2.46221445 Reorder the terms: -1.25 + x = -2.46221445 Solving -1.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.46221445 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.46221445 + 1.25 x = -2.46221445 + 1.25 Combine like terms: -2.46221445 + 1.25 = -1.21221445 x = -1.21221445 Simplifying x = -1.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.71221445, -1.21221445}Solution
x = {0, 3.71221445, -1.21221445}
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