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Simplifying 25 + -20x2 + x4 = 0 Solving 25 + -20x2 + 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 + -20x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -20x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -20x2 + x4 = 0 + -25 -20x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -20x2 + x4 = -25 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = -25 + 100 Reorder the terms: 100 + -20x2 + x4 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + -20x2 + x4 = 75 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x2 + -10) equal to 8.660254038 and -8.660254038.Subproblem 1
x2 + -10 = 8.660254038 Simplifying x2 + -10 = 8.660254038 Reorder the terms: -10 + x2 = 8.660254038 Solving -10 + x2 = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 8.660254038 + 10 x2 = 8.660254038 + 10 Combine like terms: 8.660254038 + 10 = 18.660254038 x2 = 18.660254038 Simplifying x2 = 18.660254038 Take the square root of each side: x = {-4.319751618, 4.319751618}Subproblem 2
x2 + -10 = -8.660254038 Simplifying x2 + -10 = -8.660254038 Reorder the terms: -10 + x2 = -8.660254038 Solving -10 + x2 = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -8.660254038 + 10 x2 = -8.660254038 + 10 Combine like terms: -8.660254038 + 10 = 1.339745962 x2 = 1.339745962 Simplifying x2 = 1.339745962 Take the square root of each side: x = {-1.157473957, 1.157473957}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.319751618, 4.319751618, -1.157473957, 1.157473957}
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