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Simplifying x2 + 300x + 11250 = 0 Reorder the terms: 11250 + 300x + x2 = 0 Solving 11250 + 300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11250' to each side of the equation. 11250 + 300x + -11250 + x2 = 0 + -11250 Reorder the terms: 11250 + -11250 + 300x + x2 = 0 + -11250 Combine like terms: 11250 + -11250 = 0 0 + 300x + x2 = 0 + -11250 300x + x2 = 0 + -11250 Combine like terms: 0 + -11250 = -11250 300x + x2 = -11250 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = -11250 + 22500 Reorder the terms: 22500 + 300x + x2 = -11250 + 22500 Combine like terms: -11250 + 22500 = 11250 22500 + 300x + x2 = 11250 Factor a perfect square on the left side: (x + 150)(x + 150) = 11250 Calculate the square root of the right side: 106.066017178 Break this problem into two subproblems by setting (x + 150) equal to 106.066017178 and -106.066017178.Subproblem 1
x + 150 = 106.066017178 Simplifying x + 150 = 106.066017178 Reorder the terms: 150 + x = 106.066017178 Solving 150 + x = 106.066017178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 106.066017178 + -150 Combine like terms: 150 + -150 = 0 0 + x = 106.066017178 + -150 x = 106.066017178 + -150 Combine like terms: 106.066017178 + -150 = -43.933982822 x = -43.933982822 Simplifying x = -43.933982822Subproblem 2
x + 150 = -106.066017178 Simplifying x + 150 = -106.066017178 Reorder the terms: 150 + x = -106.066017178 Solving 150 + x = -106.066017178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -106.066017178 + -150 Combine like terms: 150 + -150 = 0 0 + x = -106.066017178 + -150 x = -106.066017178 + -150 Combine like terms: -106.066017178 + -150 = -256.066017178 x = -256.066017178 Simplifying x = -256.066017178Solution
The solution to the problem is based on the solutions from the subproblems. x = {-43.933982822, -256.066017178}
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