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Simplifying 5x6 + 10x3 + -12 = 0 Reorder the terms: -12 + 10x3 + 5x6 = 0 Solving -12 + 10x3 + 5x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 2x3 + x6 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 2x3 + 2.4 + x6 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 2x3 + x6 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 2x3 + x6 = 0 + 2.4 2x3 + x6 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 2x3 + x6 = 2.4 The x term is 2x3. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x3 + 1 + x6 = 2.4 + 1 Reorder the terms: 1 + 2x3 + x6 = 2.4 + 1 Combine like terms: 2.4 + 1 = 3.4 1 + 2x3 + x6 = 3.4 Factor a perfect square on the left side: (x3 + 1)(x3 + 1) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x3 + 1) equal to 1.843908891 and -1.843908891.Subproblem 1
x3 + 1 = 1.843908891 Simplifying x3 + 1 = 1.843908891 Reorder the terms: 1 + x3 = 1.843908891 Solving 1 + x3 = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x3 = 1.843908891 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = 1.843908891 + -1 x3 = 1.843908891 + -1 Combine like terms: 1.843908891 + -1 = 0.843908891 x3 = 0.843908891 Simplifying x3 = 0.843908891 Reorder the terms: -0.843908891 + x3 = 0.843908891 + -0.843908891 Combine like terms: 0.843908891 + -0.843908891 = 0.000000000 -0.843908891 + x3 = 0.000000000 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 = -1.843908891 Simplifying x3 + 1 = -1.843908891 Reorder the terms: 1 + x3 = -1.843908891 Solving 1 + x3 = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x3 = -1.843908891 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = -1.843908891 + -1 x3 = -1.843908891 + -1 Combine like terms: -1.843908891 + -1 = -2.843908891 x3 = -2.843908891 Simplifying x3 = -2.843908891 Reorder the terms: 2.843908891 + x3 = -2.843908891 + 2.843908891 Combine like terms: -2.843908891 + 2.843908891 = 0.000000000 2.843908891 + x3 = 0.000000000 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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