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Simplifying 700 = x2 + -10x Reorder the terms: 700 = -10x + x2 Solving 700 = -10x + x2 Solving for variable 'x'. Reorder the terms: 700 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 700 + 10x + -1x2 = 0 + x2 + -1x2 700 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 700 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -700 + -10x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + -10x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + -10x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + -10x + x2 = 0 + 700 -10x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 -10x + x2 = 700 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 700 + 25 Reorder the terms: 25 + -10x + x2 = 700 + 25 Combine like terms: 700 + 25 = 725 25 + -10x + x2 = 725 Factor a perfect square on the left side: (x + -5)(x + -5) = 725 Calculate the square root of the right side: 26.925824036 Break this problem into two subproblems by setting (x + -5) equal to 26.925824036 and -26.925824036.Subproblem 1
x + -5 = 26.925824036 Simplifying x + -5 = 26.925824036 Reorder the terms: -5 + x = 26.925824036 Solving -5 + x = 26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 26.925824036 + 5 Combine like terms: -5 + 5 = 0 0 + x = 26.925824036 + 5 x = 26.925824036 + 5 Combine like terms: 26.925824036 + 5 = 31.925824036 x = 31.925824036 Simplifying x = 31.925824036Subproblem 2
x + -5 = -26.925824036 Simplifying x + -5 = -26.925824036 Reorder the terms: -5 + x = -26.925824036 Solving -5 + x = -26.925824036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -26.925824036 + 5 Combine like terms: -5 + 5 = 0 0 + x = -26.925824036 + 5 x = -26.925824036 + 5 Combine like terms: -26.925824036 + 5 = -21.925824036 x = -21.925824036 Simplifying x = -21.925824036Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.925824036, -21.925824036}
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