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Simplifying 5x4 + 15x2 = 4 Reorder the terms: 15x2 + 5x4 = 4 Solving 15x2 + 5x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + 15x2 + 5x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 15x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 3x2 + x4 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3x2 + 0.8 + x4 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3x2 + x4 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3x2 + x4 = 0 + 0.8 3x2 + x4 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3x2 + x4 = 0.8 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 0.8 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 0.8 + 2.25 Combine like terms: 0.8 + 2.25 = 3.05 2.25 + 3x2 + x4 = 3.05 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (x2 + 1.5) equal to 1.74642492 and -1.74642492.Subproblem 1
x2 + 1.5 = 1.74642492 Simplifying x2 + 1.5 = 1.74642492 Reorder the terms: 1.5 + x2 = 1.74642492 Solving 1.5 + x2 = 1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 1.74642492 + -1.5 x2 = 1.74642492 + -1.5 Combine like terms: 1.74642492 + -1.5 = 0.24642492 x2 = 0.24642492 Simplifying x2 = 0.24642492 Take the square root of each side: x = {-0.496412047, 0.496412047}Subproblem 2
x2 + 1.5 = -1.74642492 Simplifying x2 + 1.5 = -1.74642492 Reorder the terms: 1.5 + x2 = -1.74642492 Solving 1.5 + x2 = -1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -1.74642492 + -1.5 x2 = -1.74642492 + -1.5 Combine like terms: -1.74642492 + -1.5 = -3.24642492 x2 = -3.24642492 Simplifying x2 = -3.24642492 Reorder the terms: 3.24642492 + x2 = -3.24642492 + 3.24642492 Combine like terms: -3.24642492 + 3.24642492 = 0.00000000 3.24642492 + x2 = 0.00000000 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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