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Simplifying x2 + 52x + 300 = 0 Reorder the terms: 300 + 52x + x2 = 0 Solving 300 + 52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + 52x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + 52x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + 52x + x2 = 0 + -300 52x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 52x + x2 = -300 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 = -300 + 676 Reorder the terms: 676 + 52x + x2 = -300 + 676 Combine like terms: -300 + 676 = 376 676 + 52x + x2 = 376 Factor a perfect square on the left side: (x + 26)(x + 26) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + 26) equal to 19.39071943 and -19.39071943.Subproblem 1
x + 26 = 19.39071943 Simplifying x + 26 = 19.39071943 Reorder the terms: 26 + x = 19.39071943 Solving 26 + x = 19.39071943 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 = 19.39071943 + -26 Combine like terms: 26 + -26 = 0 0 + x = 19.39071943 + -26 x = 19.39071943 + -26 Combine like terms: 19.39071943 + -26 = -6.60928057 x = -6.60928057 Simplifying x = -6.60928057Subproblem 2
x + 26 = -19.39071943 Simplifying x + 26 = -19.39071943 Reorder the terms: 26 + x = -19.39071943 Solving 26 + x = -19.39071943 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 = -19.39071943 + -26 Combine like terms: 26 + -26 = 0 0 + x = -19.39071943 + -26 x = -19.39071943 + -26 Combine like terms: -19.39071943 + -26 = -45.39071943 x = -45.39071943 Simplifying x = -45.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.60928057, -45.39071943}
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