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Simplifying -1x2 + 50x + 625 = 0 Reorder the terms: 625 + 50x + -1x2 = 0 Solving 625 + 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'. -625 + -50x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -50x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -50x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -50x + x2 = 0 + 625 -50x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -50x + x2 = 625 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 = 625 + 625 Reorder the terms: 625 + -50x + x2 = 625 + 625 Combine like terms: 625 + 625 = 1250 625 + -50x + x2 = 1250 Factor a perfect square on the left side: (x + -25)(x + -25) = 1250 Calculate the square root of the right side: 35.355339059 Break this problem into two subproblems by setting (x + -25) equal to 35.355339059 and -35.355339059.Subproblem 1
x + -25 = 35.355339059 Simplifying x + -25 = 35.355339059 Reorder the terms: -25 + x = 35.355339059 Solving -25 + x = 35.355339059 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 = 35.355339059 + 25 Combine like terms: -25 + 25 = 0 0 + x = 35.355339059 + 25 x = 35.355339059 + 25 Combine like terms: 35.355339059 + 25 = 60.355339059 x = 60.355339059 Simplifying x = 60.355339059Subproblem 2
x + -25 = -35.355339059 Simplifying x + -25 = -35.355339059 Reorder the terms: -25 + x = -35.355339059 Solving -25 + x = -35.355339059 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 = -35.355339059 + 25 Combine like terms: -25 + 25 = 0 0 + x = -35.355339059 + 25 x = -35.355339059 + 25 Combine like terms: -35.355339059 + 25 = -10.355339059 x = -10.355339059 Simplifying x = -10.355339059Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.355339059, -10.355339059}
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