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Simplifying x2 + -10x + -300 = 0 Reorder the terms: -300 + -10x + x2 = 0 Solving -300 + -10x + 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 + -10x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -10x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -10x + x2 = 0 + 300 -10x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -10x + x2 = 300 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 300 + 25 Reorder the terms: 25 + -10x + x2 = 300 + 25 Combine like terms: 300 + 25 = 325 25 + -10x + x2 = 325 Factor a perfect square on the left side: (x + -5)(x + -5) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + -5) equal to 18.027756377 and -18.027756377.Subproblem 1
x + -5 = 18.027756377 Simplifying x + -5 = 18.027756377 Reorder the terms: -5 + x = 18.027756377 Solving -5 + x = 18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 18.027756377 + 5 Combine like terms: -5 + 5 = 0 0 + x = 18.027756377 + 5 x = 18.027756377 + 5 Combine like terms: 18.027756377 + 5 = 23.027756377 x = 23.027756377 Simplifying x = 23.027756377Subproblem 2
x + -5 = -18.027756377 Simplifying x + -5 = -18.027756377 Reorder the terms: -5 + x = -18.027756377 Solving -5 + x = -18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -18.027756377 + 5 Combine like terms: -5 + 5 = 0 0 + x = -18.027756377 + 5 x = -18.027756377 + 5 Combine like terms: -18.027756377 + 5 = -13.027756377 x = -13.027756377 Simplifying x = -13.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.027756377, -13.027756377}
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