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Simplifying 102 = 0.5x2 + 25x + -173 Reorder the terms: 102 = -173 + 25x + 0.5x2 Solving 102 = -173 + 25x + 0.5x2 Solving for variable 'x'. Combine like terms: 102 + 173 = 275 275 + -25x + -0.5x2 = -173 + 25x + 0.5x2 + 173 + -25x + -0.5x2 Reorder the terms: 275 + -25x + -0.5x2 = -173 + 173 + 25x + -25x + 0.5x2 + -0.5x2 Combine like terms: -173 + 173 = 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 = 1175 625 + 50x + x2 = 1175 Factor a perfect square on the left side: (x + 25)(x + 25) = 1175 Calculate the square root of the right side: 34.278273002 Break this problem into two subproblems by setting (x + 25) equal to 34.278273002 and -34.278273002.Subproblem 1
x + 25 = 34.278273002 Simplifying x + 25 = 34.278273002 Reorder the terms: 25 + x = 34.278273002 Solving 25 + x = 34.278273002 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 = 34.278273002 + -25 Combine like terms: 25 + -25 = 0 0 + x = 34.278273002 + -25 x = 34.278273002 + -25 Combine like terms: 34.278273002 + -25 = 9.278273002 x = 9.278273002 Simplifying x = 9.278273002Subproblem 2
x + 25 = -34.278273002 Simplifying x + 25 = -34.278273002 Reorder the terms: 25 + x = -34.278273002 Solving 25 + x = -34.278273002 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 = -34.278273002 + -25 Combine like terms: 25 + -25 = 0 0 + x = -34.278273002 + -25 x = -34.278273002 + -25 Combine like terms: -34.278273002 + -25 = -59.278273002 x = -59.278273002 Simplifying x = -59.278273002Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.278273002, -59.278273002}
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