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Simplifying x(x + 5) = 270 Reorder the terms: x(5 + x) = 270 (5 * x + x * x) = 270 (5x + x2) = 270 Solving 5x + x2 = 270 Solving for variable 'x'. Reorder the terms: -270 + 5x + x2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 5x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 5x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 5x + x2 = 0 + 270 5x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 5x + x2 = 270 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 270 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 270 + 6.25 Combine like terms: 270 + 6.25 = 276.25 6.25 + 5x + x2 = 276.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 276.25 Calculate the square root of the right side: 16.620770139 Break this problem into two subproblems by setting (x + 2.5) equal to 16.620770139 and -16.620770139.Subproblem 1
x + 2.5 = 16.620770139 Simplifying x + 2.5 = 16.620770139 Reorder the terms: 2.5 + x = 16.620770139 Solving 2.5 + x = 16.620770139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 16.620770139 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 16.620770139 + -2.5 x = 16.620770139 + -2.5 Combine like terms: 16.620770139 + -2.5 = 14.120770139 x = 14.120770139 Simplifying x = 14.120770139Subproblem 2
x + 2.5 = -16.620770139 Simplifying x + 2.5 = -16.620770139 Reorder the terms: 2.5 + x = -16.620770139 Solving 2.5 + x = -16.620770139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -16.620770139 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -16.620770139 + -2.5 x = -16.620770139 + -2.5 Combine like terms: -16.620770139 + -2.5 = -19.120770139 x = -19.120770139 Simplifying x = -19.120770139Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.120770139, -19.120770139}
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