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Simplifying 4x4 + 20x2 + 15 = 0 Reorder the terms: 15 + 20x2 + 4x4 = 0 Solving 15 + 20x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 5x2 + x4 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 5x2 + -3.75 + x4 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 5x2 + x4 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 5x2 + x4 = 0 + -3.75 5x2 + x4 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 5x2 + x4 = -3.75 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = -3.75 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 6.25 + 5x2 + x4 = 2.5 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x2 + 2.5) equal to 1.58113883 and -1.58113883.Subproblem 1
x2 + 2.5 = 1.58113883 Simplifying x2 + 2.5 = 1.58113883 Reorder the terms: 2.5 + x2 = 1.58113883 Solving 2.5 + x2 = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 1.58113883 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 1.58113883 + -2.5 x2 = 1.58113883 + -2.5 Combine like terms: 1.58113883 + -2.5 = -0.91886117 x2 = -0.91886117 Simplifying x2 = -0.91886117 Reorder the terms: 0.91886117 + x2 = -0.91886117 + 0.91886117 Combine like terms: -0.91886117 + 0.91886117 = 0.00000000 0.91886117 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 2.5 = -1.58113883 Simplifying x2 + 2.5 = -1.58113883 Reorder the terms: 2.5 + x2 = -1.58113883 Solving 2.5 + x2 = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -1.58113883 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -1.58113883 + -2.5 x2 = -1.58113883 + -2.5 Combine like terms: -1.58113883 + -2.5 = -4.08113883 x2 = -4.08113883 Simplifying x2 = -4.08113883 Reorder the terms: 4.08113883 + x2 = -4.08113883 + 4.08113883 Combine like terms: -4.08113883 + 4.08113883 = 0.00000000 4.08113883 + 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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