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Simplifying -1x2 + 50x + 67 = 0 Reorder the terms: 67 + 50x + -1x2 = 0 Solving 67 + 50x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -67 + -50x + x2 = 0 Move the constant term to the right: Add '67' to each side of the equation. -67 + -50x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -50x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -50x + x2 = 0 + 67 -50x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -50x + x2 = 67 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 67 + 625 Reorder the terms: 625 + -50x + x2 = 67 + 625 Combine like terms: 67 + 625 = 692 625 + -50x + x2 = 692 Factor a perfect square on the left side: (x + -25)(x + -25) = 692 Calculate the square root of the right side: 26.305892876 Break this problem into two subproblems by setting (x + -25) equal to 26.305892876 and -26.305892876.Subproblem 1
x + -25 = 26.305892876 Simplifying x + -25 = 26.305892876 Reorder the terms: -25 + x = 26.305892876 Solving -25 + x = 26.305892876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 26.305892876 + 25 Combine like terms: -25 + 25 = 0 0 + x = 26.305892876 + 25 x = 26.305892876 + 25 Combine like terms: 26.305892876 + 25 = 51.305892876 x = 51.305892876 Simplifying x = 51.305892876Subproblem 2
x + -25 = -26.305892876 Simplifying x + -25 = -26.305892876 Reorder the terms: -25 + x = -26.305892876 Solving -25 + x = -26.305892876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -26.305892876 + 25 Combine like terms: -25 + 25 = 0 0 + x = -26.305892876 + 25 x = -26.305892876 + 25 Combine like terms: -26.305892876 + 25 = -1.305892876 x = -1.305892876 Simplifying x = -1.305892876Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.305892876, -1.305892876}
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