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Simplifying x4 + 9x2 = 25 + -20 Reorder the terms: 9x2 + x4 = 25 + -20 Combine like terms: 25 + -20 = 5 9x2 + x4 = 5 Solving 9x2 + x4 = 5 Solving for variable 'x'. Reorder the terms: -5 + 9x2 + x4 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 9x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 9x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + 9x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 9x2 + x4 = 0 + 5 9x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 9x2 + x4 = 5 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 = 5 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = 5 + 20.25 Combine like terms: 5 + 20.25 = 25.25 20.25 + 9x2 + x4 = 25.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x2 + 4.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x2 + 4.5 = 5.024937811 Simplifying x2 + 4.5 = 5.024937811 Reorder the terms: 4.5 + x2 = 5.024937811 Solving 4.5 + x2 = 5.024937811 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 = 5.024937811 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 5.024937811 + -4.5 x2 = 5.024937811 + -4.5 Combine like terms: 5.024937811 + -4.5 = 0.524937811 x2 = 0.524937811 Simplifying x2 = 0.524937811 Take the square root of each side: x = {-0.724525922, 0.724525922}Subproblem 2
x2 + 4.5 = -5.024937811 Simplifying x2 + 4.5 = -5.024937811 Reorder the terms: 4.5 + x2 = -5.024937811 Solving 4.5 + x2 = -5.024937811 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 = -5.024937811 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -5.024937811 + -4.5 x2 = -5.024937811 + -4.5 Combine like terms: -5.024937811 + -4.5 = -9.524937811 x2 = -9.524937811 Simplifying x2 = -9.524937811 Reorder the terms: 9.524937811 + x2 = -9.524937811 + 9.524937811 Combine like terms: -9.524937811 + 9.524937811 = 0.000000000 9.524937811 + 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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