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Simplifying x2 + -300x + 5625 = 0 Reorder the terms: 5625 + -300x + x2 = 0 Solving 5625 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5625' to each side of the equation. 5625 + -300x + -5625 + x2 = 0 + -5625 Reorder the terms: 5625 + -5625 + -300x + x2 = 0 + -5625 Combine like terms: 5625 + -5625 = 0 0 + -300x + x2 = 0 + -5625 -300x + x2 = 0 + -5625 Combine like terms: 0 + -5625 = -5625 -300x + x2 = -5625 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 = -5625 + 22500 Reorder the terms: 22500 + -300x + x2 = -5625 + 22500 Combine like terms: -5625 + 22500 = 16875 22500 + -300x + x2 = 16875 Factor a perfect square on the left side: (x + -150)(x + -150) = 16875 Calculate the square root of the right side: 129.903810568 Break this problem into two subproblems by setting (x + -150) equal to 129.903810568 and -129.903810568.Subproblem 1
x + -150 = 129.903810568 Simplifying x + -150 = 129.903810568 Reorder the terms: -150 + x = 129.903810568 Solving -150 + x = 129.903810568 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 = 129.903810568 + 150 Combine like terms: -150 + 150 = 0 0 + x = 129.903810568 + 150 x = 129.903810568 + 150 Combine like terms: 129.903810568 + 150 = 279.903810568 x = 279.903810568 Simplifying x = 279.903810568Subproblem 2
x + -150 = -129.903810568 Simplifying x + -150 = -129.903810568 Reorder the terms: -150 + x = -129.903810568 Solving -150 + x = -129.903810568 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 = -129.903810568 + 150 Combine like terms: -150 + 150 = 0 0 + x = -129.903810568 + 150 x = -129.903810568 + 150 Combine like terms: -129.903810568 + 150 = 20.096189432 x = 20.096189432 Simplifying x = 20.096189432Solution
The solution to the problem is based on the solutions from the subproblems. x = {279.903810568, 20.096189432}
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