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Simplifying X2 + -52X + -25 = 0 Reorder the terms: -25 + -52X + X2 = 0 Solving -25 + -52X + X2 = 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 + -52X + 25 + X2 = 0 + 25 Reorder the terms: -25 + 25 + -52X + X2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -52X + X2 = 0 + 25 -52X + X2 = 0 + 25 Combine like terms: 0 + 25 = 25 -52X + X2 = 25 The X term is -52X. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52X + 676 + X2 = 25 + 676 Reorder the terms: 676 + -52X + X2 = 25 + 676 Combine like terms: 25 + 676 = 701 676 + -52X + X2 = 701 Factor a perfect square on the left side: (X + -26)(X + -26) = 701 Calculate the square root of the right side: 26.47640459 Break this problem into two subproblems by setting (X + -26) equal to 26.47640459 and -26.47640459.Subproblem 1
X + -26 = 26.47640459 Simplifying X + -26 = 26.47640459 Reorder the terms: -26 + X = 26.47640459 Solving -26 + X = 26.47640459 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + X = 26.47640459 + 26 Combine like terms: -26 + 26 = 0 0 + X = 26.47640459 + 26 X = 26.47640459 + 26 Combine like terms: 26.47640459 + 26 = 52.47640459 X = 52.47640459 Simplifying X = 52.47640459Subproblem 2
X + -26 = -26.47640459 Simplifying X + -26 = -26.47640459 Reorder the terms: -26 + X = -26.47640459 Solving -26 + X = -26.47640459 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + X = -26.47640459 + 26 Combine like terms: -26 + 26 = 0 0 + X = -26.47640459 + 26 X = -26.47640459 + 26 Combine like terms: -26.47640459 + 26 = -0.47640459 X = -0.47640459 Simplifying X = -0.47640459Solution
The solution to the problem is based on the solutions from the subproblems. X = {52.47640459, -0.47640459}
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