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Simplifying 4x4 + 28x2 + -49 = 0 Reorder the terms: -49 + 28x2 + 4x4 = 0 Solving -49 + 28x2 + 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'. -12.25 + 7x2 + x4 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + 7x2 + 12.25 + x4 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + 7x2 + x4 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + 7x2 + x4 = 0 + 12.25 7x2 + x4 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 7x2 + x4 = 12.25 The x term is 7x2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x2 + 12.25 + x4 = 12.25 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = 12.25 + 12.25 Combine like terms: 12.25 + 12.25 = 24.5 12.25 + 7x2 + x4 = 24.5 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (x2 + 3.5) equal to 4.949747468 and -4.949747468.Subproblem 1
x2 + 3.5 = 4.949747468 Simplifying x2 + 3.5 = 4.949747468 Reorder the terms: 3.5 + x2 = 4.949747468 Solving 3.5 + x2 = 4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = 4.949747468 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 4.949747468 + -3.5 x2 = 4.949747468 + -3.5 Combine like terms: 4.949747468 + -3.5 = 1.449747468 x2 = 1.449747468 Simplifying x2 = 1.449747468 Take the square root of each side: x = {-1.204054595, 1.204054595}Subproblem 2
x2 + 3.5 = -4.949747468 Simplifying x2 + 3.5 = -4.949747468 Reorder the terms: 3.5 + x2 = -4.949747468 Solving 3.5 + x2 = -4.949747468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = -4.949747468 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -4.949747468 + -3.5 x2 = -4.949747468 + -3.5 Combine like terms: -4.949747468 + -3.5 = -8.449747468 x2 = -8.449747468 Simplifying x2 = -8.449747468 Reorder the terms: 8.449747468 + x2 = -8.449747468 + 8.449747468 Combine like terms: -8.449747468 + 8.449747468 = 0.000000000 8.449747468 + 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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