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Simplifying 15x4 + 15x2 + 15 = 233 Reorder the terms: 15 + 15x2 + 15x4 = 233 Solving 15 + 15x2 + 15x4 = 233 Solving for variable 'x'. Reorder the terms: 15 + -233 + 15x2 + 15x4 = 233 + -233 Combine like terms: 15 + -233 = -218 -218 + 15x2 + 15x4 = 233 + -233 Combine like terms: 233 + -233 = 0 -218 + 15x2 + 15x4 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -14.53333333 + x2 + x4 = 0 Move the constant term to the right: Add '14.53333333' to each side of the equation. -14.53333333 + x2 + 14.53333333 + x4 = 0 + 14.53333333 Reorder the terms: -14.53333333 + 14.53333333 + x2 + x4 = 0 + 14.53333333 Combine like terms: -14.53333333 + 14.53333333 = 0.00000000 0.00000000 + x2 + x4 = 0 + 14.53333333 x2 + x4 = 0 + 14.53333333 Combine like terms: 0 + 14.53333333 = 14.53333333 x2 + x4 = 14.53333333 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 = 14.53333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 14.53333333 + 0.25 Combine like terms: 14.53333333 + 0.25 = 14.78333333 1.25 + x4 = 14.78333333 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 14.78333333 Calculate the square root of the right side: 3.844910055 Break this problem into two subproblems by setting (x2 + 0.5) equal to 3.844910055 and -3.844910055.Subproblem 1
x2 + 0.5 = 3.844910055 Simplifying x2 + 0.5 = 3.844910055 Reorder the terms: 0.5 + x2 = 3.844910055 Solving 0.5 + x2 = 3.844910055 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 = 3.844910055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 3.844910055 + -0.5 x2 = 3.844910055 + -0.5 Combine like terms: 3.844910055 + -0.5 = 3.344910055 x2 = 3.344910055 Simplifying x2 = 3.344910055 Take the square root of each side: x = {-1.828909526, 1.828909526}Subproblem 2
x2 + 0.5 = -3.844910055 Simplifying x2 + 0.5 = -3.844910055 Reorder the terms: 0.5 + x2 = -3.844910055 Solving 0.5 + x2 = -3.844910055 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 = -3.844910055 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -3.844910055 + -0.5 x2 = -3.844910055 + -0.5 Combine like terms: -3.844910055 + -0.5 = -4.344910055 x2 = -4.344910055 Simplifying x2 = -4.344910055 Reorder the terms: 4.344910055 + x2 = -4.344910055 + 4.344910055 Combine like terms: -4.344910055 + 4.344910055 = 0.000000000 4.344910055 + 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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