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Simplifying 2x4 + -7.6x2 + -1.6 = 0 Reorder the terms: -1.6 + -7.6x2 + 2x4 = 0 Solving -1.6 + -7.6x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.8 + -3.8x2 + x4 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -3.8x2 + 0.8 + x4 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -3.8x2 + x4 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -3.8x2 + x4 = 0 + 0.8 -3.8x2 + x4 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -3.8x2 + x4 = 0.8 The x term is -3.8x2. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x2 + 3.61 + x4 = 0.8 + 3.61 Reorder the terms: 3.61 + -3.8x2 + x4 = 0.8 + 3.61 Combine like terms: 0.8 + 3.61 = 4.41 3.61 + -3.8x2 + x4 = 4.41 Factor a perfect square on the left side: (x2 + -1.9)(x2 + -1.9) = 4.41 Calculate the square root of the right side: 2.1 Break this problem into two subproblems by setting (x2 + -1.9) equal to 2.1 and -2.1.Subproblem 1
x2 + -1.9 = 2.1 Simplifying x2 + -1.9 = 2.1 Reorder the terms: -1.9 + x2 = 2.1 Solving -1.9 + x2 = 2.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x2 = 2.1 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x2 = 2.1 + 1.9 x2 = 2.1 + 1.9 Combine like terms: 2.1 + 1.9 = 4 x2 = 4 Simplifying x2 = 4 Take the square root of each side: x = {-2, 2}Subproblem 2
x2 + -1.9 = -2.1 Simplifying x2 + -1.9 = -2.1 Reorder the terms: -1.9 + x2 = -2.1 Solving -1.9 + x2 = -2.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x2 = -2.1 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x2 = -2.1 + 1.9 x2 = -2.1 + 1.9 Combine like terms: -2.1 + 1.9 = -0.2 x2 = -0.2 Simplifying x2 = -0.2 Reorder the terms: 0.2 + x2 = -0.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.2 + x2 = 0.0 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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