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Simplifying x2 + 10x = 300 Reorder the terms: 10x + x2 = 300 Solving 10x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 10x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 10x + x2 = 0 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 = 13.027756377 x = 13.027756377 Simplifying x = 13.027756377Subproblem 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 = -23.027756377 x = -23.027756377 Simplifying x = -23.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.027756377, -23.027756377}
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