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Simplifying 900 = (x + 30) * x Reorder the terms: 900 = (30 + x) * x Reorder the terms for easier multiplication: 900 = x(30 + x) 900 = (30 * x + x * x) 900 = (30x + x2) Solving 900 = 30x + x2 Solving for variable 'x'. Reorder the terms: 900 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 900 + -30x + -1x2 = 0 + x2 + -1x2 900 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 900 + -30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -900 + 30x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 30x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 30x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 30x + x2 = 0 + 900 30x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 30x + x2 = 900 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 = 900 + 225 Reorder the terms: 225 + 30x + x2 = 900 + 225 Combine like terms: 900 + 225 = 1125 225 + 30x + x2 = 1125 Factor a perfect square on the left side: (x + 15)(x + 15) = 1125 Calculate the square root of the right side: 33.541019662 Break this problem into two subproblems by setting (x + 15) equal to 33.541019662 and -33.541019662.Subproblem 1
x + 15 = 33.541019662 Simplifying x + 15 = 33.541019662 Reorder the terms: 15 + x = 33.541019662 Solving 15 + x = 33.541019662 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 = 33.541019662 + -15 Combine like terms: 15 + -15 = 0 0 + x = 33.541019662 + -15 x = 33.541019662 + -15 Combine like terms: 33.541019662 + -15 = 18.541019662 x = 18.541019662 Simplifying x = 18.541019662Subproblem 2
x + 15 = -33.541019662 Simplifying x + 15 = -33.541019662 Reorder the terms: 15 + x = -33.541019662 Solving 15 + x = -33.541019662 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 = -33.541019662 + -15 Combine like terms: 15 + -15 = 0 0 + x = -33.541019662 + -15 x = -33.541019662 + -15 Combine like terms: -33.541019662 + -15 = -48.541019662 x = -48.541019662 Simplifying x = -48.541019662Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.541019662, -48.541019662}
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