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Simplifying x2 + 280x + -300 = 0 Reorder the terms: -300 + 280x + x2 = 0 Solving -300 + 280x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 280x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 280x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 280x + x2 = 0 + 300 280x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 280x + x2 = 300 The x term is 280x. Take half its coefficient (140). Square it (19600) and add it to both sides. Add '19600' to each side of the equation. 280x + 19600 + x2 = 300 + 19600 Reorder the terms: 19600 + 280x + x2 = 300 + 19600 Combine like terms: 300 + 19600 = 19900 19600 + 280x + x2 = 19900 Factor a perfect square on the left side: (x + 140)(x + 140) = 19900 Calculate the square root of the right side: 141.067359797 Break this problem into two subproblems by setting (x + 140) equal to 141.067359797 and -141.067359797.Subproblem 1
x + 140 = 141.067359797 Simplifying x + 140 = 141.067359797 Reorder the terms: 140 + x = 141.067359797 Solving 140 + x = 141.067359797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = 141.067359797 + -140 Combine like terms: 140 + -140 = 0 0 + x = 141.067359797 + -140 x = 141.067359797 + -140 Combine like terms: 141.067359797 + -140 = 1.067359797 x = 1.067359797 Simplifying x = 1.067359797Subproblem 2
x + 140 = -141.067359797 Simplifying x + 140 = -141.067359797 Reorder the terms: 140 + x = -141.067359797 Solving 140 + x = -141.067359797 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = -141.067359797 + -140 Combine like terms: 140 + -140 = 0 0 + x = -141.067359797 + -140 x = -141.067359797 + -140 Combine like terms: -141.067359797 + -140 = -281.067359797 x = -281.067359797 Simplifying x = -281.067359797Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.067359797, -281.067359797}
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