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Simplifying 4x6 + -2x3 = 9 Reorder the terms: -2x3 + 4x6 = 9 Solving -2x3 + 4x6 = 9 Solving for variable 'x'. Reorder the terms: -9 + -2x3 + 4x6 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -2x3 + 4x6 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -0.5x3 + x6 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.5x3 + 2.25 + x6 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.5x3 + x6 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.5x3 + x6 = 0 + 2.25 -0.5x3 + x6 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.5x3 + x6 = 2.25 The x term is -0.5x3. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x3 + 0.0625 + x6 = 2.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x3 + x6 = 2.25 + 0.0625 Combine like terms: 2.25 + 0.0625 = 2.3125 0.0625 + -0.5x3 + x6 = 2.3125 Factor a perfect square on the left side: (x3 + -0.25)(x3 + -0.25) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x3 + -0.25) equal to 1.520690633 and -1.520690633.Subproblem 1
x3 + -0.25 = 1.520690633 Simplifying x3 + -0.25 = 1.520690633 Reorder the terms: -0.25 + x3 = 1.520690633 Solving -0.25 + x3 = 1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x3 = 1.520690633 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x3 = 1.520690633 + 0.25 x3 = 1.520690633 + 0.25 Combine like terms: 1.520690633 + 0.25 = 1.770690633 x3 = 1.770690633 Simplifying x3 = 1.770690633 Reorder the terms: -1.770690633 + x3 = 1.770690633 + -1.770690633 Combine like terms: 1.770690633 + -1.770690633 = 0.000000000 -1.770690633 + 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 + -0.25 = -1.520690633 Simplifying x3 + -0.25 = -1.520690633 Reorder the terms: -0.25 + x3 = -1.520690633 Solving -0.25 + x3 = -1.520690633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x3 = -1.520690633 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x3 = -1.520690633 + 0.25 x3 = -1.520690633 + 0.25 Combine like terms: -1.520690633 + 0.25 = -1.270690633 x3 = -1.270690633 Simplifying x3 = -1.270690633 Reorder the terms: 1.270690633 + x3 = -1.270690633 + 1.270690633 Combine like terms: -1.270690633 + 1.270690633 = 0.000000000 1.270690633 + 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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