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Simplifying x(x + 30) = 3600 Reorder the terms: x(30 + x) = 3600 (30 * x + x * x) = 3600 (30x + x2) = 3600 Solving 30x + x2 = 3600 Solving for variable 'x'. Reorder the terms: -3600 + 30x + x2 = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3600 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 30x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 30x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 30x + x2 = 0 + 3600 30x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 30x + x2 = 3600 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 = 3600 + 225 Reorder the terms: 225 + 30x + x2 = 3600 + 225 Combine like terms: 3600 + 225 = 3825 225 + 30x + x2 = 3825 Factor a perfect square on the left side: (x + 15)(x + 15) = 3825 Calculate the square root of the right side: 61.846584384 Break this problem into two subproblems by setting (x + 15) equal to 61.846584384 and -61.846584384.Subproblem 1
x + 15 = 61.846584384 Simplifying x + 15 = 61.846584384 Reorder the terms: 15 + x = 61.846584384 Solving 15 + x = 61.846584384 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 = 61.846584384 + -15 Combine like terms: 15 + -15 = 0 0 + x = 61.846584384 + -15 x = 61.846584384 + -15 Combine like terms: 61.846584384 + -15 = 46.846584384 x = 46.846584384 Simplifying x = 46.846584384Subproblem 2
x + 15 = -61.846584384 Simplifying x + 15 = -61.846584384 Reorder the terms: 15 + x = -61.846584384 Solving 15 + x = -61.846584384 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 = -61.846584384 + -15 Combine like terms: 15 + -15 = 0 0 + x = -61.846584384 + -15 x = -61.846584384 + -15 Combine like terms: -61.846584384 + -15 = -76.846584384 x = -76.846584384 Simplifying x = -76.846584384Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.846584384, -76.846584384}
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