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Simplifying x2 + -40x + 325 = 0 Reorder the terms: 325 + -40x + x2 = 0 Solving 325 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-325' to each side of the equation. 325 + -40x + -325 + x2 = 0 + -325 Reorder the terms: 325 + -325 + -40x + x2 = 0 + -325 Combine like terms: 325 + -325 = 0 0 + -40x + x2 = 0 + -325 -40x + x2 = 0 + -325 Combine like terms: 0 + -325 = -325 -40x + x2 = -325 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -325 + 400 Reorder the terms: 400 + -40x + x2 = -325 + 400 Combine like terms: -325 + 400 = 75 400 + -40x + x2 = 75 Factor a perfect square on the left side: (x + -20)(x + -20) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -20) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -20 = 8.660254038 Simplifying x + -20 = 8.660254038 Reorder the terms: -20 + x = 8.660254038 Solving -20 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 8.660254038 + 20 Combine like terms: -20 + 20 = 0 0 + x = 8.660254038 + 20 x = 8.660254038 + 20 Combine like terms: 8.660254038 + 20 = 28.660254038 x = 28.660254038 Simplifying x = 28.660254038Subproblem 2
x + -20 = -8.660254038 Simplifying x + -20 = -8.660254038 Reorder the terms: -20 + x = -8.660254038 Solving -20 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -8.660254038 + 20 Combine like terms: -20 + 20 = 0 0 + x = -8.660254038 + 20 x = -8.660254038 + 20 Combine like terms: -8.660254038 + 20 = 11.339745962 x = 11.339745962 Simplifying x = 11.339745962Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.660254038, 11.339745962}
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