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Simplifying -1x2 + 50x + 700 = 0 Reorder the terms: 700 + 50x + -1x2 = 0 Solving 700 + 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'. -700 + -50x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + -50x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + -50x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + -50x + x2 = 0 + 700 -50x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 -50x + x2 = 700 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 = 700 + 625 Reorder the terms: 625 + -50x + x2 = 700 + 625 Combine like terms: 700 + 625 = 1325 625 + -50x + x2 = 1325 Factor a perfect square on the left side: (x + -25)(x + -25) = 1325 Calculate the square root of the right side: 36.400549446 Break this problem into two subproblems by setting (x + -25) equal to 36.400549446 and -36.400549446.Subproblem 1
x + -25 = 36.400549446 Simplifying x + -25 = 36.400549446 Reorder the terms: -25 + x = 36.400549446 Solving -25 + x = 36.400549446 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 = 36.400549446 + 25 Combine like terms: -25 + 25 = 0 0 + x = 36.400549446 + 25 x = 36.400549446 + 25 Combine like terms: 36.400549446 + 25 = 61.400549446 x = 61.400549446 Simplifying x = 61.400549446Subproblem 2
x + -25 = -36.400549446 Simplifying x + -25 = -36.400549446 Reorder the terms: -25 + x = -36.400549446 Solving -25 + x = -36.400549446 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 = -36.400549446 + 25 Combine like terms: -25 + 25 = 0 0 + x = -36.400549446 + 25 x = -36.400549446 + 25 Combine like terms: -36.400549446 + 25 = -11.400549446 x = -11.400549446 Simplifying x = -11.400549446Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.400549446, -11.400549446}
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