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Simplifying 105 = -0.5x2 + 25x + -170 Reorder the terms: 105 = -170 + 25x + -0.5x2 Solving 105 = -170 + 25x + -0.5x2 Solving for variable 'x'. Combine like terms: 105 + 170 = 275 275 + -25x + 0.5x2 = -170 + 25x + -0.5x2 + 170 + -25x + 0.5x2 Reorder the terms: 275 + -25x + 0.5x2 = -170 + 170 + 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: -170 + 170 = 0 275 + -25x + 0.5x2 = 0 + 25x + -25x + -0.5x2 + 0.5x2 275 + -25x + 0.5x2 = 25x + -25x + -0.5x2 + 0.5x2 Combine like terms: 25x + -25x = 0 275 + -25x + 0.5x2 = 0 + -0.5x2 + 0.5x2 275 + -25x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 275 + -25x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 550 + -50x + x2 = 0 Move the constant term to the right: Add '-550' to each side of the equation. 550 + -50x + -550 + x2 = 0 + -550 Reorder the terms: 550 + -550 + -50x + x2 = 0 + -550 Combine like terms: 550 + -550 = 0 0 + -50x + x2 = 0 + -550 -50x + x2 = 0 + -550 Combine like terms: 0 + -550 = -550 -50x + x2 = -550 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 = -550 + 625 Reorder the terms: 625 + -50x + x2 = -550 + 625 Combine like terms: -550 + 625 = 75 625 + -50x + x2 = 75 Factor a perfect square on the left side: (x + -25)(x + -25) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -25) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -25 = 8.660254038 Simplifying x + -25 = 8.660254038 Reorder the terms: -25 + x = 8.660254038 Solving -25 + x = 8.660254038 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 = 8.660254038 + 25 Combine like terms: -25 + 25 = 0 0 + x = 8.660254038 + 25 x = 8.660254038 + 25 Combine like terms: 8.660254038 + 25 = 33.660254038 x = 33.660254038 Simplifying x = 33.660254038Subproblem 2
x + -25 = -8.660254038 Simplifying x + -25 = -8.660254038 Reorder the terms: -25 + x = -8.660254038 Solving -25 + x = -8.660254038 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 = -8.660254038 + 25 Combine like terms: -25 + 25 = 0 0 + x = -8.660254038 + 25 x = -8.660254038 + 25 Combine like terms: -8.660254038 + 25 = 16.339745962 x = 16.339745962 Simplifying x = 16.339745962Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.660254038, 16.339745962}
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