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Simplifying 0 = 5x4 + -45x2 + -12 Reorder the terms: 0 = -12 + -45x2 + 5x4 Solving 0 = -12 + -45x2 + 5x4 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + 45x2 + -5x4 = -12 + -45x2 + 5x4 + 12 + 45x2 + -5x4 Reorder the terms: 12 + 45x2 + -5x4 = -12 + 12 + -45x2 + 45x2 + 5x4 + -5x4 Combine like terms: -12 + 12 = 0 12 + 45x2 + -5x4 = 0 + -45x2 + 45x2 + 5x4 + -5x4 12 + 45x2 + -5x4 = -45x2 + 45x2 + 5x4 + -5x4 Combine like terms: -45x2 + 45x2 = 0 12 + 45x2 + -5x4 = 0 + 5x4 + -5x4 12 + 45x2 + -5x4 = 5x4 + -5x4 Combine like terms: 5x4 + -5x4 = 0 12 + 45x2 + -5x4 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -9x2 + x4 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -9x2 + 2.4 + x4 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -9x2 + x4 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -9x2 + x4 = 0 + 2.4 -9x2 + x4 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -9x2 + x4 = 2.4 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = 2.4 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 2.4 + 20.25 Combine like terms: 2.4 + 20.25 = 22.65 20.25 + -9x2 + x4 = 22.65 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 22.65 Calculate the square root of the right side: 4.759201614 Break this problem into two subproblems by setting (x2 + -4.5) equal to 4.759201614 and -4.759201614.Subproblem 1
x2 + -4.5 = 4.759201614 Simplifying x2 + -4.5 = 4.759201614 Reorder the terms: -4.5 + x2 = 4.759201614 Solving -4.5 + x2 = 4.759201614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 4.759201614 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.759201614 + 4.5 x2 = 4.759201614 + 4.5 Combine like terms: 4.759201614 + 4.5 = 9.259201614 x2 = 9.259201614 Simplifying x2 = 9.259201614 Take the square root of each side: x = {-3.042893625, 3.042893625}Subproblem 2
x2 + -4.5 = -4.759201614 Simplifying x2 + -4.5 = -4.759201614 Reorder the terms: -4.5 + x2 = -4.759201614 Solving -4.5 + x2 = -4.759201614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -4.759201614 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.759201614 + 4.5 x2 = -4.759201614 + 4.5 Combine like terms: -4.759201614 + 4.5 = -0.259201614 x2 = -0.259201614 Simplifying x2 = -0.259201614 Reorder the terms: 0.259201614 + x2 = -0.259201614 + 0.259201614 Combine like terms: -0.259201614 + 0.259201614 = 0.000000000 0.259201614 + 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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