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Simplifying -700 = x2 + -264x Reorder the terms: -700 = -264x + x2 Solving -700 = -264x + x2 Solving for variable 'x'. Reorder the terms: -700 + 264x + -1x2 = -264x + 264x + x2 + -1x2 Combine like terms: -264x + 264x = 0 -700 + 264x + -1x2 = 0 + x2 + -1x2 -700 + 264x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -700 + 264x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 700 + -264x + x2 = 0 Move the constant term to the right: Add '-700' to each side of the equation. 700 + -264x + -700 + x2 = 0 + -700 Reorder the terms: 700 + -700 + -264x + x2 = 0 + -700 Combine like terms: 700 + -700 = 0 0 + -264x + x2 = 0 + -700 -264x + x2 = 0 + -700 Combine like terms: 0 + -700 = -700 -264x + x2 = -700 The x term is -264x. Take half its coefficient (-132). Square it (17424) and add it to both sides. Add '17424' to each side of the equation. -264x + 17424 + x2 = -700 + 17424 Reorder the terms: 17424 + -264x + x2 = -700 + 17424 Combine like terms: -700 + 17424 = 16724 17424 + -264x + x2 = 16724 Factor a perfect square on the left side: (x + -132)(x + -132) = 16724 Calculate the square root of the right side: 129.321305283 Break this problem into two subproblems by setting (x + -132) equal to 129.321305283 and -129.321305283.Subproblem 1
x + -132 = 129.321305283 Simplifying x + -132 = 129.321305283 Reorder the terms: -132 + x = 129.321305283 Solving -132 + x = 129.321305283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '132' to each side of the equation. -132 + 132 + x = 129.321305283 + 132 Combine like terms: -132 + 132 = 0 0 + x = 129.321305283 + 132 x = 129.321305283 + 132 Combine like terms: 129.321305283 + 132 = 261.321305283 x = 261.321305283 Simplifying x = 261.321305283Subproblem 2
x + -132 = -129.321305283 Simplifying x + -132 = -129.321305283 Reorder the terms: -132 + x = -129.321305283 Solving -132 + x = -129.321305283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '132' to each side of the equation. -132 + 132 + x = -129.321305283 + 132 Combine like terms: -132 + 132 = 0 0 + x = -129.321305283 + 132 x = -129.321305283 + 132 Combine like terms: -129.321305283 + 132 = 2.678694717 x = 2.678694717 Simplifying x = 2.678694717Solution
The solution to the problem is based on the solutions from the subproblems. x = {261.321305283, 2.678694717}
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