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Simplifying x(x + 3) = 225 Reorder the terms: x(3 + x) = 225 (3 * x + x * x) = 225 (3x + x2) = 225 Solving 3x + x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 3x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 3x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 3x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 3x + x2 = 0 + 225 3x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 3x + x2 = 225 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 225 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 225 + 2.25 Combine like terms: 225 + 2.25 = 227.25 2.25 + 3x + x2 = 227.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 227.25 Calculate the square root of the right side: 15.074813432 Break this problem into two subproblems by setting (x + 1.5) equal to 15.074813432 and -15.074813432.Subproblem 1
x + 1.5 = 15.074813432 Simplifying x + 1.5 = 15.074813432 Reorder the terms: 1.5 + x = 15.074813432 Solving 1.5 + x = 15.074813432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 15.074813432 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 15.074813432 + -1.5 x = 15.074813432 + -1.5 Combine like terms: 15.074813432 + -1.5 = 13.574813432 x = 13.574813432 Simplifying x = 13.574813432Subproblem 2
x + 1.5 = -15.074813432 Simplifying x + 1.5 = -15.074813432 Reorder the terms: 1.5 + x = -15.074813432 Solving 1.5 + x = -15.074813432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -15.074813432 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -15.074813432 + -1.5 x = -15.074813432 + -1.5 Combine like terms: -15.074813432 + -1.5 = -16.574813432 x = -16.574813432 Simplifying x = -16.574813432Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.574813432, -16.574813432}
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