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Simplifying 5x3 + 2x6 + -9 = 0 Reorder the terms: -9 + 5x3 + 2x6 = 0 Solving -9 + 5x3 + 2x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 2.5x3 + x6 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2.5x3 + 4.5 + x6 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2.5x3 + x6 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2.5x3 + x6 = 0 + 4.5 2.5x3 + x6 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2.5x3 + x6 = 4.5 The x term is 2.5x3. 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. 2.5x3 + 1.5625 + x6 = 4.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x3 + x6 = 4.5 + 1.5625 Combine like terms: 4.5 + 1.5625 = 6.0625 1.5625 + 2.5x3 + x6 = 6.0625 Factor a perfect square on the left side: (x3 + 1.25)(x3 + 1.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x3 + 1.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x3 + 1.25 = 2.46221445 Simplifying x3 + 1.25 = 2.46221445 Reorder the terms: 1.25 + x3 = 2.46221445 Solving 1.25 + x3 = 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 + x3 = 2.46221445 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x3 = 2.46221445 + -1.25 x3 = 2.46221445 + -1.25 Combine like terms: 2.46221445 + -1.25 = 1.21221445 x3 = 1.21221445 Simplifying x3 = 1.21221445 Reorder the terms: -1.21221445 + x3 = 1.21221445 + -1.21221445 Combine like terms: 1.21221445 + -1.21221445 = 0.00000000 -1.21221445 + x3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 1.25 = -2.46221445 Simplifying x3 + 1.25 = -2.46221445 Reorder the terms: 1.25 + x3 = -2.46221445 Solving 1.25 + x3 = -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 + x3 = -2.46221445 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x3 = -2.46221445 + -1.25 x3 = -2.46221445 + -1.25 Combine like terms: -2.46221445 + -1.25 = -3.71221445 x3 = -3.71221445 Simplifying x3 = -3.71221445 Reorder the terms: 3.71221445 + x3 = -3.71221445 + 3.71221445 Combine like terms: -3.71221445 + 3.71221445 = 0.00000000 3.71221445 + x3 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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