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Simplifying x2 + 30x + -100 = 0 Reorder the terms: -100 + 30x + x2 = 0 Solving -100 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 30x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 30x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 30x + x2 = 0 + 100 30x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 30x + x2 = 100 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 100 + 225 Reorder the terms: 225 + 30x + x2 = 100 + 225 Combine like terms: 100 + 225 = 325 225 + 30x + x2 = 325 Factor a perfect square on the left side: (x + 15)(x + 15) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + 15) equal to 18.027756377 and -18.027756377.Subproblem 1
x + 15 = 18.027756377 Simplifying x + 15 = 18.027756377 Reorder the terms: 15 + x = 18.027756377 Solving 15 + x = 18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 18.027756377 + -15 Combine like terms: 15 + -15 = 0 0 + x = 18.027756377 + -15 x = 18.027756377 + -15 Combine like terms: 18.027756377 + -15 = 3.027756377 x = 3.027756377 Simplifying x = 3.027756377Subproblem 2
x + 15 = -18.027756377 Simplifying x + 15 = -18.027756377 Reorder the terms: 15 + x = -18.027756377 Solving 15 + x = -18.027756377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -18.027756377 + -15 Combine like terms: 15 + -15 = 0 0 + x = -18.027756377 + -15 x = -18.027756377 + -15 Combine like terms: -18.027756377 + -15 = -33.027756377 x = -33.027756377 Simplifying x = -33.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.027756377, -33.027756377}
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