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Simplifying x2 + 30x + -49 = 0 Reorder the terms: -49 + 30x + x2 = 0 Solving -49 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 30x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + 30x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 30x + x2 = 0 + 49 30x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 30x + x2 = 49 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 = 49 + 225 Reorder the terms: 225 + 30x + x2 = 49 + 225 Combine like terms: 49 + 225 = 274 225 + 30x + x2 = 274 Factor a perfect square on the left side: (x + 15)(x + 15) = 274 Calculate the square root of the right side: 16.552945357 Break this problem into two subproblems by setting (x + 15) equal to 16.552945357 and -16.552945357.Subproblem 1
x + 15 = 16.552945357 Simplifying x + 15 = 16.552945357 Reorder the terms: 15 + x = 16.552945357 Solving 15 + x = 16.552945357 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 = 16.552945357 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.552945357 + -15 x = 16.552945357 + -15 Combine like terms: 16.552945357 + -15 = 1.552945357 x = 1.552945357 Simplifying x = 1.552945357Subproblem 2
x + 15 = -16.552945357 Simplifying x + 15 = -16.552945357 Reorder the terms: 15 + x = -16.552945357 Solving 15 + x = -16.552945357 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 = -16.552945357 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.552945357 + -15 x = -16.552945357 + -15 Combine like terms: -16.552945357 + -15 = -31.552945357 x = -31.552945357 Simplifying x = -31.552945357Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.552945357, -31.552945357}
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