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Simplifying x(x + 6) = 300 Reorder the terms: x(6 + x) = 300 (6 * x + x * x) = 300 (6x + x2) = 300 Solving 6x + x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 6x + x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 6x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 6x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 6x + x2 = 0 + 300 6x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 6x + x2 = 300 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 300 + 9 Reorder the terms: 9 + 6x + x2 = 300 + 9 Combine like terms: 300 + 9 = 309 9 + 6x + x2 = 309 Factor a perfect square on the left side: (x + 3)(x + 3) = 309 Calculate the square root of the right side: 17.578395831 Break this problem into two subproblems by setting (x + 3) equal to 17.578395831 and -17.578395831.Subproblem 1
x + 3 = 17.578395831 Simplifying x + 3 = 17.578395831 Reorder the terms: 3 + x = 17.578395831 Solving 3 + x = 17.578395831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + x = 17.578395831 + -3 x = 17.578395831 + -3 Combine like terms: 17.578395831 + -3 = 14.578395831 x = 14.578395831 Simplifying x = 14.578395831Subproblem 2
x + 3 = -17.578395831 Simplifying x + 3 = -17.578395831 Reorder the terms: 3 + x = -17.578395831 Solving 3 + x = -17.578395831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -17.578395831 + -3 Combine like terms: 3 + -3 = 0 0 + x = -17.578395831 + -3 x = -17.578395831 + -3 Combine like terms: -17.578395831 + -3 = -20.578395831 x = -20.578395831 Simplifying x = -20.578395831Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.578395831, -20.578395831}
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