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Simplifying 15x4 + -60x2 = 1 Reorder the terms: -60x2 + 15x4 = 1 Solving -60x2 + 15x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + -60x2 + 15x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -60x2 + 15x4 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.06666666667 + -4x2 + x4 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -4x2 + 0.06666666667 + x4 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -4x2 + x4 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -4x2 + x4 = 0 + 0.06666666667 -4x2 + x4 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -4x2 + x4 = 0.06666666667 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 = 0.06666666667 + 4 Reorder the terms: 4 + -4x2 + x4 = 0.06666666667 + 4 Combine like terms: 0.06666666667 + 4 = 4.06666666667 4 + -4x2 + x4 = 4.06666666667 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 4.06666666667 Calculate the square root of the right side: 2.016597795 Break this problem into two subproblems by setting (x2 + -2) equal to 2.016597795 and -2.016597795.Subproblem 1
x2 + -2 = 2.016597795 Simplifying x2 + -2 = 2.016597795 Reorder the terms: -2 + x2 = 2.016597795 Solving -2 + x2 = 2.016597795 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 = 2.016597795 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.016597795 + 2 x2 = 2.016597795 + 2 Combine like terms: 2.016597795 + 2 = 4.016597795 x2 = 4.016597795 Simplifying x2 = 4.016597795 Take the square root of each side: x = {-2.004145153, 2.004145153}Subproblem 2
x2 + -2 = -2.016597795 Simplifying x2 + -2 = -2.016597795 Reorder the terms: -2 + x2 = -2.016597795 Solving -2 + x2 = -2.016597795 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 = -2.016597795 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.016597795 + 2 x2 = -2.016597795 + 2 Combine like terms: -2.016597795 + 2 = -0.016597795 x2 = -0.016597795 Simplifying x2 = -0.016597795 Reorder the terms: 0.016597795 + x2 = -0.016597795 + 0.016597795 Combine like terms: -0.016597795 + 0.016597795 = 0.000000000 0.016597795 + 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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