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Simplifying 2x2 + 41x + 207 = 594 Reorder the terms: 207 + 41x + 2x2 = 594 Solving 207 + 41x + 2x2 = 594 Solving for variable 'x'. Reorder the terms: 207 + -594 + 41x + 2x2 = 594 + -594 Combine like terms: 207 + -594 = -387 -387 + 41x + 2x2 = 594 + -594 Combine like terms: 594 + -594 = 0 -387 + 41x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -193.5 + 20.5x + x2 = 0 Move the constant term to the right: Add '193.5' to each side of the equation. -193.5 + 20.5x + 193.5 + x2 = 0 + 193.5 Reorder the terms: -193.5 + 193.5 + 20.5x + x2 = 0 + 193.5 Combine like terms: -193.5 + 193.5 = 0.0 0.0 + 20.5x + x2 = 0 + 193.5 20.5x + x2 = 0 + 193.5 Combine like terms: 0 + 193.5 = 193.5 20.5x + x2 = 193.5 The x term is 20.5x. Take half its coefficient (10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. 20.5x + 105.0625 + x2 = 193.5 + 105.0625 Reorder the terms: 105.0625 + 20.5x + x2 = 193.5 + 105.0625 Combine like terms: 193.5 + 105.0625 = 298.5625 105.0625 + 20.5x + x2 = 298.5625 Factor a perfect square on the left side: (x + 10.25)(x + 10.25) = 298.5625 Calculate the square root of the right side: 17.278961196 Break this problem into two subproblems by setting (x + 10.25) equal to 17.278961196 and -17.278961196.Subproblem 1
x + 10.25 = 17.278961196 Simplifying x + 10.25 = 17.278961196 Reorder the terms: 10.25 + x = 17.278961196 Solving 10.25 + x = 17.278961196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = 17.278961196 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = 17.278961196 + -10.25 x = 17.278961196 + -10.25 Combine like terms: 17.278961196 + -10.25 = 7.028961196 x = 7.028961196 Simplifying x = 7.028961196Subproblem 2
x + 10.25 = -17.278961196 Simplifying x + 10.25 = -17.278961196 Reorder the terms: 10.25 + x = -17.278961196 Solving 10.25 + x = -17.278961196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = -17.278961196 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = -17.278961196 + -10.25 x = -17.278961196 + -10.25 Combine like terms: -17.278961196 + -10.25 = -27.528961196 x = -27.528961196 Simplifying x = -27.528961196Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.028961196, -27.528961196}
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