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Simplifying x2 + -300x + 2600 = 0 Reorder the terms: 2600 + -300x + x2 = 0 Solving 2600 + -300x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2600' to each side of the equation. 2600 + -300x + -2600 + x2 = 0 + -2600 Reorder the terms: 2600 + -2600 + -300x + x2 = 0 + -2600 Combine like terms: 2600 + -2600 = 0 0 + -300x + x2 = 0 + -2600 -300x + x2 = 0 + -2600 Combine like terms: 0 + -2600 = -2600 -300x + x2 = -2600 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 = -2600 + 22500 Reorder the terms: 22500 + -300x + x2 = -2600 + 22500 Combine like terms: -2600 + 22500 = 19900 22500 + -300x + x2 = 19900 Factor a perfect square on the left side: (x + -150)(x + -150) = 19900 Calculate the square root of the right side: 141.067359797 Break this problem into two subproblems by setting (x + -150) equal to 141.067359797 and -141.067359797.Subproblem 1
x + -150 = 141.067359797 Simplifying x + -150 = 141.067359797 Reorder the terms: -150 + x = 141.067359797 Solving -150 + x = 141.067359797 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 = 141.067359797 + 150 Combine like terms: -150 + 150 = 0 0 + x = 141.067359797 + 150 x = 141.067359797 + 150 Combine like terms: 141.067359797 + 150 = 291.067359797 x = 291.067359797 Simplifying x = 291.067359797Subproblem 2
x + -150 = -141.067359797 Simplifying x + -150 = -141.067359797 Reorder the terms: -150 + x = -141.067359797 Solving -150 + x = -141.067359797 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 = -141.067359797 + 150 Combine like terms: -150 + 150 = 0 0 + x = -141.067359797 + 150 x = -141.067359797 + 150 Combine like terms: -141.067359797 + 150 = 8.932640203 x = 8.932640203 Simplifying x = 8.932640203Solution
The solution to the problem is based on the solutions from the subproblems. x = {291.067359797, 8.932640203}
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