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Simplifying 15x4 + -60x2 + -14 = 0 Reorder the terms: -14 + -60x2 + 15x4 = 0 Solving -14 + -60x2 + 15x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.9333333333 + -4x2 + x4 = 0 Move the constant term to the right: Add '0.9333333333' to each side of the equation. -0.9333333333 + -4x2 + 0.9333333333 + x4 = 0 + 0.9333333333 Reorder the terms: -0.9333333333 + 0.9333333333 + -4x2 + x4 = 0 + 0.9333333333 Combine like terms: -0.9333333333 + 0.9333333333 = 0.0000000000 0.0000000000 + -4x2 + x4 = 0 + 0.9333333333 -4x2 + x4 = 0 + 0.9333333333 Combine like terms: 0 + 0.9333333333 = 0.9333333333 -4x2 + x4 = 0.9333333333 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 0.9333333333 + 4 Reorder the terms: 4 + -4x2 + x4 = 0.9333333333 + 4 Combine like terms: 0.9333333333 + 4 = 4.9333333333 4 + -4x2 + x4 = 4.9333333333 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 4.9333333333 Calculate the square root of the right side: 2.221110833 Break this problem into two subproblems by setting (x2 + -2) equal to 2.221110833 and -2.221110833.Subproblem 1
x2 + -2 = 2.221110833 Simplifying x2 + -2 = 2.221110833 Reorder the terms: -2 + x2 = 2.221110833 Solving -2 + x2 = 2.221110833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.221110833 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.221110833 + 2 x2 = 2.221110833 + 2 Combine like terms: 2.221110833 + 2 = 4.221110833 x2 = 4.221110833 Simplifying x2 = 4.221110833 Take the square root of each side: x = {-2.054534213, 2.054534213}Subproblem 2
x2 + -2 = -2.221110833 Simplifying x2 + -2 = -2.221110833 Reorder the terms: -2 + x2 = -2.221110833 Solving -2 + x2 = -2.221110833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.221110833 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.221110833 + 2 x2 = -2.221110833 + 2 Combine like terms: -2.221110833 + 2 = -0.221110833 x2 = -0.221110833 Simplifying x2 = -0.221110833 Reorder the terms: 0.221110833 + x2 = -0.221110833 + 0.221110833 Combine like terms: -0.221110833 + 0.221110833 = 0.000000000 0.221110833 + 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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