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Simplifying 2x4 + -11x2 + -15 = 0 Reorder the terms: -15 + -11x2 + 2x4 = 0 Solving -15 + -11x2 + 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'. -7.5 + -5.5x2 + x4 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5.5x2 + 7.5 + x4 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5.5x2 + x4 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5.5x2 + x4 = 0 + 7.5 -5.5x2 + x4 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5.5x2 + x4 = 7.5 The x term is -5.5x2. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x2 + 7.5625 + x4 = 7.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x2 + x4 = 7.5 + 7.5625 Combine like terms: 7.5 + 7.5625 = 15.0625 7.5625 + -5.5x2 + x4 = 15.0625 Factor a perfect square on the left side: (x2 + -2.75)(x2 + -2.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x2 + -2.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x2 + -2.75 = 3.881043674 Simplifying x2 + -2.75 = 3.881043674 Reorder the terms: -2.75 + x2 = 3.881043674 Solving -2.75 + x2 = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x2 = 3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x2 = 3.881043674 + 2.75 x2 = 3.881043674 + 2.75 Combine like terms: 3.881043674 + 2.75 = 6.631043674 x2 = 6.631043674 Simplifying x2 = 6.631043674 Take the square root of each side: x = {-2.575081295, 2.575081295}Subproblem 2
x2 + -2.75 = -3.881043674 Simplifying x2 + -2.75 = -3.881043674 Reorder the terms: -2.75 + x2 = -3.881043674 Solving -2.75 + x2 = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x2 = -3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x2 = -3.881043674 + 2.75 x2 = -3.881043674 + 2.75 Combine like terms: -3.881043674 + 2.75 = -1.131043674 x2 = -1.131043674 Simplifying x2 = -1.131043674 Reorder the terms: 1.131043674 + x2 = -1.131043674 + 1.131043674 Combine like terms: -1.131043674 + 1.131043674 = 0.000000000 1.131043674 + 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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