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Simplifying 5135.5 = 3.5x2 + 364x + -965 Reorder the terms: 5135.5 = -965 + 364x + 3.5x2 Solving 5135.5 = -965 + 364x + 3.5x2 Solving for variable 'x'. Combine like terms: 5135.5 + 965 = 6100.5 6100.5 + -364x + -3.5x2 = -965 + 364x + 3.5x2 + 965 + -364x + -3.5x2 Reorder the terms: 6100.5 + -364x + -3.5x2 = -965 + 965 + 364x + -364x + 3.5x2 + -3.5x2 Combine like terms: -965 + 965 = 0 6100.5 + -364x + -3.5x2 = 0 + 364x + -364x + 3.5x2 + -3.5x2 6100.5 + -364x + -3.5x2 = 364x + -364x + 3.5x2 + -3.5x2 Combine like terms: 364x + -364x = 0 6100.5 + -364x + -3.5x2 = 0 + 3.5x2 + -3.5x2 6100.5 + -364x + -3.5x2 = 3.5x2 + -3.5x2 Combine like terms: 3.5x2 + -3.5x2 = 0.0 6100.5 + -364x + -3.5x2 = 0.0 Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -1743 + 104x + x2 = 0 Move the constant term to the right: Add '1743' to each side of the equation. -1743 + 104x + 1743 + x2 = 0 + 1743 Reorder the terms: -1743 + 1743 + 104x + x2 = 0 + 1743 Combine like terms: -1743 + 1743 = 0 0 + 104x + x2 = 0 + 1743 104x + x2 = 0 + 1743 Combine like terms: 0 + 1743 = 1743 104x + x2 = 1743 The x term is 104x. Take half its coefficient (52). Square it (2704) and add it to both sides. Add '2704' to each side of the equation. 104x + 2704 + x2 = 1743 + 2704 Reorder the terms: 2704 + 104x + x2 = 1743 + 2704 Combine like terms: 1743 + 2704 = 4447 2704 + 104x + x2 = 4447 Factor a perfect square on the left side: (x + 52)(x + 52) = 4447 Calculate the square root of the right side: 66.685830579 Break this problem into two subproblems by setting (x + 52) equal to 66.685830579 and -66.685830579.Subproblem 1
x + 52 = 66.685830579 Simplifying x + 52 = 66.685830579 Reorder the terms: 52 + x = 66.685830579 Solving 52 + x = 66.685830579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -52 + x = 66.685830579 + -52 Combine like terms: 52 + -52 = 0 0 + x = 66.685830579 + -52 x = 66.685830579 + -52 Combine like terms: 66.685830579 + -52 = 14.685830579 x = 14.685830579 Simplifying x = 14.685830579Subproblem 2
x + 52 = -66.685830579 Simplifying x + 52 = -66.685830579 Reorder the terms: 52 + x = -66.685830579 Solving 52 + x = -66.685830579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -52 + x = -66.685830579 + -52 Combine like terms: 52 + -52 = 0 0 + x = -66.685830579 + -52 x = -66.685830579 + -52 Combine like terms: -66.685830579 + -52 = -118.685830579 x = -118.685830579 Simplifying x = -118.685830579Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.685830579, -118.685830579}
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