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Simplifying x2 + 30x + -225 = 0 Reorder the terms: -225 + 30x + x2 = 0 Solving -225 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 30x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 30x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 30x + x2 = 0 + 225 30x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 30x + x2 = 225 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 = 225 + 225 Reorder the terms: 225 + 30x + x2 = 225 + 225 Combine like terms: 225 + 225 = 450 225 + 30x + x2 = 450 Factor a perfect square on the left side: (x + 15)(x + 15) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 15) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 15 = 21.213203436 Simplifying x + 15 = 21.213203436 Reorder the terms: 15 + x = 21.213203436 Solving 15 + x = 21.213203436 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 = 21.213203436 + -15 Combine like terms: 15 + -15 = 0 0 + x = 21.213203436 + -15 x = 21.213203436 + -15 Combine like terms: 21.213203436 + -15 = 6.213203436 x = 6.213203436 Simplifying x = 6.213203436Subproblem 2
x + 15 = -21.213203436 Simplifying x + 15 = -21.213203436 Reorder the terms: 15 + x = -21.213203436 Solving 15 + x = -21.213203436 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 = -21.213203436 + -15 Combine like terms: 15 + -15 = 0 0 + x = -21.213203436 + -15 x = -21.213203436 + -15 Combine like terms: -21.213203436 + -15 = -36.213203436 x = -36.213203436 Simplifying x = -36.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.213203436, -36.213203436}
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