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Simplifying x2 + 52x = 672 Reorder the terms: 52x + x2 = 672 Solving 52x + x2 = 672 Solving for variable 'x'. Reorder the terms: -672 + 52x + x2 = 672 + -672 Combine like terms: 672 + -672 = 0 -672 + 52x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '672' to each side of the equation. -672 + 52x + 672 + x2 = 0 + 672 Reorder the terms: -672 + 672 + 52x + x2 = 0 + 672 Combine like terms: -672 + 672 = 0 0 + 52x + x2 = 0 + 672 52x + x2 = 0 + 672 Combine like terms: 0 + 672 = 672 52x + x2 = 672 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 = 672 + 676 Reorder the terms: 676 + 52x + x2 = 672 + 676 Combine like terms: 672 + 676 = 1348 676 + 52x + x2 = 1348 Factor a perfect square on the left side: (x + 26)(x + 26) = 1348 Calculate the square root of the right side: 36.715119501 Break this problem into two subproblems by setting (x + 26) equal to 36.715119501 and -36.715119501.Subproblem 1
x + 26 = 36.715119501 Simplifying x + 26 = 36.715119501 Reorder the terms: 26 + x = 36.715119501 Solving 26 + x = 36.715119501 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 = 36.715119501 + -26 Combine like terms: 26 + -26 = 0 0 + x = 36.715119501 + -26 x = 36.715119501 + -26 Combine like terms: 36.715119501 + -26 = 10.715119501 x = 10.715119501 Simplifying x = 10.715119501Subproblem 2
x + 26 = -36.715119501 Simplifying x + 26 = -36.715119501 Reorder the terms: 26 + x = -36.715119501 Solving 26 + x = -36.715119501 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 = -36.715119501 + -26 Combine like terms: 26 + -26 = 0 0 + x = -36.715119501 + -26 x = -36.715119501 + -26 Combine like terms: -36.715119501 + -26 = -62.715119501 x = -62.715119501 Simplifying x = -62.715119501Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.715119501, -62.715119501}
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