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Simplifying x2 + -58x + -168 = 0 Reorder the terms: -168 + -58x + x2 = 0 Solving -168 + -58x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + -58x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -58x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -58x + x2 = 0 + 168 -58x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -58x + x2 = 168 The x term is -58x. Take half its coefficient (-29). Square it (841) and add it to both sides. Add '841' to each side of the equation. -58x + 841 + x2 = 168 + 841 Reorder the terms: 841 + -58x + x2 = 168 + 841 Combine like terms: 168 + 841 = 1009 841 + -58x + x2 = 1009 Factor a perfect square on the left side: (x + -29)(x + -29) = 1009 Calculate the square root of the right side: 31.764760349 Break this problem into two subproblems by setting (x + -29) equal to 31.764760349 and -31.764760349.Subproblem 1
x + -29 = 31.764760349 Simplifying x + -29 = 31.764760349 Reorder the terms: -29 + x = 31.764760349 Solving -29 + x = 31.764760349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + x = 31.764760349 + 29 Combine like terms: -29 + 29 = 0 0 + x = 31.764760349 + 29 x = 31.764760349 + 29 Combine like terms: 31.764760349 + 29 = 60.764760349 x = 60.764760349 Simplifying x = 60.764760349Subproblem 2
x + -29 = -31.764760349 Simplifying x + -29 = -31.764760349 Reorder the terms: -29 + x = -31.764760349 Solving -29 + x = -31.764760349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + x = -31.764760349 + 29 Combine like terms: -29 + 29 = 0 0 + x = -31.764760349 + 29 x = -31.764760349 + 29 Combine like terms: -31.764760349 + 29 = -2.764760349 x = -2.764760349 Simplifying x = -2.764760349Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.764760349, -2.764760349}
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