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Simplifying 15x4 + 15x2 + 15 = 23 Reorder the terms: 15 + 15x2 + 15x4 = 23 Solving 15 + 15x2 + 15x4 = 23 Solving for variable 'x'. Reorder the terms: 15 + -23 + 15x2 + 15x4 = 23 + -23 Combine like terms: 15 + -23 = -8 -8 + 15x2 + 15x4 = 23 + -23 Combine like terms: 23 + -23 = 0 -8 + 15x2 + 15x4 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + x2 + x4 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + x2 + 0.5333333333 + x4 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + x2 + x4 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + x2 + x4 = 0 + 0.5333333333 x2 + x4 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 x2 + x4 = 0.5333333333 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x4 = 0.5333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 0.5333333333 + 0.25 Combine like terms: 0.5333333333 + 0.25 = 0.7833333333 1.25 + x4 = 0.7833333333 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 0.7833333333 Calculate the square root of the right side: 0.885061203 Break this problem into two subproblems by setting (x2 + 0.5) equal to 0.885061203 and -0.885061203.Subproblem 1
x2 + 0.5 = 0.885061203 Simplifying x2 + 0.5 = 0.885061203 Reorder the terms: 0.5 + x2 = 0.885061203 Solving 0.5 + x2 = 0.885061203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 0.885061203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 0.885061203 + -0.5 x2 = 0.885061203 + -0.5 Combine like terms: 0.885061203 + -0.5 = 0.385061203 x2 = 0.385061203 Simplifying x2 = 0.385061203 Take the square root of each side: x = {-0.620532999, 0.620532999}Subproblem 2
x2 + 0.5 = -0.885061203 Simplifying x2 + 0.5 = -0.885061203 Reorder the terms: 0.5 + x2 = -0.885061203 Solving 0.5 + x2 = -0.885061203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -0.885061203 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -0.885061203 + -0.5 x2 = -0.885061203 + -0.5 Combine like terms: -0.885061203 + -0.5 = -1.385061203 x2 = -1.385061203 Simplifying x2 = -1.385061203 Reorder the terms: 1.385061203 + x2 = -1.385061203 + 1.385061203 Combine like terms: -1.385061203 + 1.385061203 = 0.000000000 1.385061203 + x2 = 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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