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Simplifying x2 + -300x + -30000 = 0 Reorder the terms: -30000 + -300x + x2 = 0 Solving -30000 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30000' to each side of the equation. -30000 + -300x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + -300x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + -300x + x2 = 0 + 30000 -300x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 -300x + x2 = 30000 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 = 30000 + 22500 Reorder the terms: 22500 + -300x + x2 = 30000 + 22500 Combine like terms: 30000 + 22500 = 52500 22500 + -300x + x2 = 52500 Factor a perfect square on the left side: (x + -150)(x + -150) = 52500 Calculate the square root of the right side: 229.128784748 Break this problem into two subproblems by setting (x + -150) equal to 229.128784748 and -229.128784748.Subproblem 1
x + -150 = 229.128784748 Simplifying x + -150 = 229.128784748 Reorder the terms: -150 + x = 229.128784748 Solving -150 + x = 229.128784748 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 = 229.128784748 + 150 Combine like terms: -150 + 150 = 0 0 + x = 229.128784748 + 150 x = 229.128784748 + 150 Combine like terms: 229.128784748 + 150 = 379.128784748 x = 379.128784748 Simplifying x = 379.128784748Subproblem 2
x + -150 = -229.128784748 Simplifying x + -150 = -229.128784748 Reorder the terms: -150 + x = -229.128784748 Solving -150 + x = -229.128784748 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 = -229.128784748 + 150 Combine like terms: -150 + 150 = 0 0 + x = -229.128784748 + 150 x = -229.128784748 + 150 Combine like terms: -229.128784748 + 150 = -79.128784748 x = -79.128784748 Simplifying x = -79.128784748Solution
The solution to the problem is based on the solutions from the subproblems. x = {379.128784748, -79.128784748}
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