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Simplifying x4 + -1x2 + -25 = 0 Reorder the terms: -25 + -1x2 + x4 = 0 Solving -25 + -1x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -1x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + -1x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x2 + x4 = 0 + 25 -1x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 -1x2 + x4 = 25 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 25 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 25 + 0.25 Combine like terms: 25 + 0.25 = 25.25 0.25 + -1x2 + x4 = 25.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x2 + -0.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x2 + -0.5 = 5.024937811 Simplifying x2 + -0.5 = 5.024937811 Reorder the terms: -0.5 + x2 = 5.024937811 Solving -0.5 + x2 = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 5.024937811 + 0.5 x2 = 5.024937811 + 0.5 Combine like terms: 5.024937811 + 0.5 = 5.524937811 x2 = 5.524937811 Simplifying x2 = 5.524937811 Take the square root of each side: x = {-2.350518626, 2.350518626}Subproblem 2
x2 + -0.5 = -5.024937811 Simplifying x2 + -0.5 = -5.024937811 Reorder the terms: -0.5 + x2 = -5.024937811 Solving -0.5 + x2 = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -5.024937811 + 0.5 x2 = -5.024937811 + 0.5 Combine like terms: -5.024937811 + 0.5 = -4.524937811 x2 = -4.524937811 Simplifying x2 = -4.524937811 Reorder the terms: 4.524937811 + x2 = -4.524937811 + 4.524937811 Combine like terms: -4.524937811 + 4.524937811 = 0.000000000 4.524937811 + 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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