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Simplifying x2 + 52x + -400 = 0 Reorder the terms: -400 + 52x + x2 = 0 Solving -400 + 52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 52x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 52x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 52x + x2 = 0 + 400 52x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 52x + x2 = 400 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 = 400 + 676 Reorder the terms: 676 + 52x + x2 = 400 + 676 Combine like terms: 400 + 676 = 1076 676 + 52x + x2 = 1076 Factor a perfect square on the left side: (x + 26)(x + 26) = 1076 Calculate the square root of the right side: 32.802438934 Break this problem into two subproblems by setting (x + 26) equal to 32.802438934 and -32.802438934.Subproblem 1
x + 26 = 32.802438934 Simplifying x + 26 = 32.802438934 Reorder the terms: 26 + x = 32.802438934 Solving 26 + x = 32.802438934 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 = 32.802438934 + -26 Combine like terms: 26 + -26 = 0 0 + x = 32.802438934 + -26 x = 32.802438934 + -26 Combine like terms: 32.802438934 + -26 = 6.802438934 x = 6.802438934 Simplifying x = 6.802438934Subproblem 2
x + 26 = -32.802438934 Simplifying x + 26 = -32.802438934 Reorder the terms: 26 + x = -32.802438934 Solving 26 + x = -32.802438934 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 = -32.802438934 + -26 Combine like terms: 26 + -26 = 0 0 + x = -32.802438934 + -26 x = -32.802438934 + -26 Combine like terms: -32.802438934 + -26 = -58.802438934 x = -58.802438934 Simplifying x = -58.802438934Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.802438934, -58.802438934}
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