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Simplifying x2 + -48x + -300 = 0 Reorder the terms: -300 + -48x + x2 = 0 Solving -300 + -48x + 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 + -48x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -48x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -48x + x2 = 0 + 300 -48x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -48x + x2 = 300 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 300 + 576 Reorder the terms: 576 + -48x + x2 = 300 + 576 Combine like terms: 300 + 576 = 876 576 + -48x + x2 = 876 Factor a perfect square on the left side: (x + -24)(x + -24) = 876 Calculate the square root of the right side: 29.597297174 Break this problem into two subproblems by setting (x + -24) equal to 29.597297174 and -29.597297174.Subproblem 1
x + -24 = 29.597297174 Simplifying x + -24 = 29.597297174 Reorder the terms: -24 + x = 29.597297174 Solving -24 + x = 29.597297174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 29.597297174 + 24 Combine like terms: -24 + 24 = 0 0 + x = 29.597297174 + 24 x = 29.597297174 + 24 Combine like terms: 29.597297174 + 24 = 53.597297174 x = 53.597297174 Simplifying x = 53.597297174Subproblem 2
x + -24 = -29.597297174 Simplifying x + -24 = -29.597297174 Reorder the terms: -24 + x = -29.597297174 Solving -24 + x = -29.597297174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -29.597297174 + 24 Combine like terms: -24 + 24 = 0 0 + x = -29.597297174 + 24 x = -29.597297174 + 24 Combine like terms: -29.597297174 + 24 = -5.597297174 x = -5.597297174 Simplifying x = -5.597297174Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.597297174, -5.597297174}
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