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Simplifying x2 + 30x + 109 = 0 Reorder the terms: 109 + 30x + x2 = 0 Solving 109 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-109' to each side of the equation. 109 + 30x + -109 + x2 = 0 + -109 Reorder the terms: 109 + -109 + 30x + x2 = 0 + -109 Combine like terms: 109 + -109 = 0 0 + 30x + x2 = 0 + -109 30x + x2 = 0 + -109 Combine like terms: 0 + -109 = -109 30x + x2 = -109 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 = -109 + 225 Reorder the terms: 225 + 30x + x2 = -109 + 225 Combine like terms: -109 + 225 = 116 225 + 30x + x2 = 116 Factor a perfect square on the left side: (x + 15)(x + 15) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 15) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 15 = 10.770329614 Simplifying x + 15 = 10.770329614 Reorder the terms: 15 + x = 10.770329614 Solving 15 + x = 10.770329614 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 = 10.770329614 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.770329614 + -15 x = 10.770329614 + -15 Combine like terms: 10.770329614 + -15 = -4.229670386 x = -4.229670386 Simplifying x = -4.229670386Subproblem 2
x + 15 = -10.770329614 Simplifying x + 15 = -10.770329614 Reorder the terms: 15 + x = -10.770329614 Solving 15 + x = -10.770329614 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 = -10.770329614 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.770329614 + -15 x = -10.770329614 + -15 Combine like terms: -10.770329614 + -15 = -25.770329614 x = -25.770329614 Simplifying x = -25.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.229670386, -25.770329614}
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