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Simplifying x2 + 30x + -450 = 0 Reorder the terms: -450 + 30x + x2 = 0 Solving -450 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 30x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 30x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 30x + x2 = 0 + 450 30x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 30x + x2 = 450 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 = 450 + 225 Reorder the terms: 225 + 30x + x2 = 450 + 225 Combine like terms: 450 + 225 = 675 225 + 30x + x2 = 675 Factor a perfect square on the left side: (x + 15)(x + 15) = 675 Calculate the square root of the right side: 25.980762114 Break this problem into two subproblems by setting (x + 15) equal to 25.980762114 and -25.980762114.Subproblem 1
x + 15 = 25.980762114 Simplifying x + 15 = 25.980762114 Reorder the terms: 15 + x = 25.980762114 Solving 15 + x = 25.980762114 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 = 25.980762114 + -15 Combine like terms: 15 + -15 = 0 0 + x = 25.980762114 + -15 x = 25.980762114 + -15 Combine like terms: 25.980762114 + -15 = 10.980762114 x = 10.980762114 Simplifying x = 10.980762114Subproblem 2
x + 15 = -25.980762114 Simplifying x + 15 = -25.980762114 Reorder the terms: 15 + x = -25.980762114 Solving 15 + x = -25.980762114 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 = -25.980762114 + -15 Combine like terms: 15 + -15 = 0 0 + x = -25.980762114 + -15 x = -25.980762114 + -15 Combine like terms: -25.980762114 + -15 = -40.980762114 x = -40.980762114 Simplifying x = -40.980762114Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.980762114, -40.980762114}
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