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Simplifying x2 + 300x + -4400 = 0 Reorder the terms: -4400 + 300x + x2 = 0 Solving -4400 + 300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4400' to each side of the equation. -4400 + 300x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + 300x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + 300x + x2 = 0 + 4400 300x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 300x + x2 = 4400 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 = 4400 + 22500 Reorder the terms: 22500 + 300x + x2 = 4400 + 22500 Combine like terms: 4400 + 22500 = 26900 22500 + 300x + x2 = 26900 Factor a perfect square on the left side: (x + 150)(x + 150) = 26900 Calculate the square root of the right side: 164.012194669 Break this problem into two subproblems by setting (x + 150) equal to 164.012194669 and -164.012194669.Subproblem 1
x + 150 = 164.012194669 Simplifying x + 150 = 164.012194669 Reorder the terms: 150 + x = 164.012194669 Solving 150 + x = 164.012194669 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 = 164.012194669 + -150 Combine like terms: 150 + -150 = 0 0 + x = 164.012194669 + -150 x = 164.012194669 + -150 Combine like terms: 164.012194669 + -150 = 14.012194669 x = 14.012194669 Simplifying x = 14.012194669Subproblem 2
x + 150 = -164.012194669 Simplifying x + 150 = -164.012194669 Reorder the terms: 150 + x = -164.012194669 Solving 150 + x = -164.012194669 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 = -164.012194669 + -150 Combine like terms: 150 + -150 = 0 0 + x = -164.012194669 + -150 x = -164.012194669 + -150 Combine like terms: -164.012194669 + -150 = -314.012194669 x = -314.012194669 Simplifying x = -314.012194669Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.012194669, -314.012194669}
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