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Simplifying 0.25x6 = 4x3 + -15 Reorder the terms: 0.25x6 = -15 + 4x3 Solving 0.25x6 = -15 + 4x3 Solving for variable 'x'. Reorder the terms: 15 + -4x3 + 0.25x6 = -15 + 4x3 + 15 + -4x3 Reorder the terms: 15 + -4x3 + 0.25x6 = -15 + 15 + 4x3 + -4x3 Combine like terms: -15 + 15 = 0 15 + -4x3 + 0.25x6 = 0 + 4x3 + -4x3 15 + -4x3 + 0.25x6 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 15 + -4x3 + 0.25x6 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 60 + -16x3 + x6 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -16x3 + -60 + x6 = 0 + -60 Reorder the terms: 60 + -60 + -16x3 + x6 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -16x3 + x6 = 0 + -60 -16x3 + x6 = 0 + -60 Combine like terms: 0 + -60 = -60 -16x3 + x6 = -60 The x term is -16x3. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x3 + 64 + x6 = -60 + 64 Reorder the terms: 64 + -16x3 + x6 = -60 + 64 Combine like terms: -60 + 64 = 4 64 + -16x3 + x6 = 4 Factor a perfect square on the left side: (x3 + -8)(x3 + -8) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x3 + -8) equal to 2 and -2.Subproblem 1
x3 + -8 = 2 Simplifying x3 + -8 = 2 Reorder the terms: -8 + x3 = 2 Solving -8 + x3 = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x3 = 2 + 8 Combine like terms: -8 + 8 = 0 0 + x3 = 2 + 8 x3 = 2 + 8 Combine like terms: 2 + 8 = 10 x3 = 10 Simplifying x3 = 10 Reorder the terms: -10 + x3 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + x3 = 0 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + -8 = -2 Simplifying x3 + -8 = -2 Reorder the terms: -8 + x3 = -2 Solving -8 + x3 = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x3 = -2 + 8 Combine like terms: -8 + 8 = 0 0 + x3 = -2 + 8 x3 = -2 + 8 Combine like terms: -2 + 8 = 6 x3 = 6 Simplifying x3 = 6 Reorder the terms: -6 + x3 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + x3 = 0 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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