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Simplifying 600 = 0.90x2 + -26.5x + 290 Reorder the terms: 600 = 290 + -26.5x + 0.90x2 Solving 600 = 290 + -26.5x + 0.90x2 Solving for variable 'x'. Combine like terms: 600 + -290 = 310 310 + 26.5x + -0.90x2 = 290 + -26.5x + 0.90x2 + -290 + 26.5x + -0.90x2 Reorder the terms: 310 + 26.5x + -0.90x2 = 290 + -290 + -26.5x + 26.5x + 0.90x2 + -0.90x2 Combine like terms: 290 + -290 = 0 310 + 26.5x + -0.90x2 = 0 + -26.5x + 26.5x + 0.90x2 + -0.90x2 310 + 26.5x + -0.90x2 = -26.5x + 26.5x + 0.90x2 + -0.90x2 Combine like terms: -26.5x + 26.5x = 0.0 310 + 26.5x + -0.90x2 = 0.0 + 0.90x2 + -0.90x2 310 + 26.5x + -0.90x2 = 0.90x2 + -0.90x2 Combine like terms: 0.90x2 + -0.90x2 = 0.00 310 + 26.5x + -0.90x2 = 0.00 Begin completing the square. Divide all terms by -0.90 the coefficient of the squared term: Divide each side by '-0.90'. -344.4444444 + -29.44444444x + x2 = 0 Move the constant term to the right: Add '344.4444444' to each side of the equation. -344.4444444 + -29.44444444x + 344.4444444 + x2 = 0 + 344.4444444 Reorder the terms: -344.4444444 + 344.4444444 + -29.44444444x + x2 = 0 + 344.4444444 Combine like terms: -344.4444444 + 344.4444444 = 0.0000000 0.0000000 + -29.44444444x + x2 = 0 + 344.4444444 -29.44444444x + x2 = 0 + 344.4444444 Combine like terms: 0 + 344.4444444 = 344.4444444 -29.44444444x + x2 = 344.4444444 The x term is -29.44444444x. Take half its coefficient (-14.72222222). Square it (216.7438271) and add it to both sides. Add '216.7438271' to each side of the equation. -29.44444444x + 216.7438271 + x2 = 344.4444444 + 216.7438271 Reorder the terms: 216.7438271 + -29.44444444x + x2 = 344.4444444 + 216.7438271 Combine like terms: 344.4444444 + 216.7438271 = 561.1882715 216.7438271 + -29.44444444x + x2 = 561.1882715 Factor a perfect square on the left side: (x + -14.72222222)(x + -14.72222222) = 561.1882715 Calculate the square root of the right side: 23.689412646 Break this problem into two subproblems by setting (x + -14.72222222) equal to 23.689412646 and -23.689412646.Subproblem 1
x + -14.72222222 = 23.689412646 Simplifying x + -14.72222222 = 23.689412646 Reorder the terms: -14.72222222 + x = 23.689412646 Solving -14.72222222 + x = 23.689412646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72222222' to each side of the equation. -14.72222222 + 14.72222222 + x = 23.689412646 + 14.72222222 Combine like terms: -14.72222222 + 14.72222222 = 0.00000000 0.00000000 + x = 23.689412646 + 14.72222222 x = 23.689412646 + 14.72222222 Combine like terms: 23.689412646 + 14.72222222 = 38.411634866 x = 38.411634866 Simplifying x = 38.411634866Subproblem 2
x + -14.72222222 = -23.689412646 Simplifying x + -14.72222222 = -23.689412646 Reorder the terms: -14.72222222 + x = -23.689412646 Solving -14.72222222 + x = -23.689412646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.72222222' to each side of the equation. -14.72222222 + 14.72222222 + x = -23.689412646 + 14.72222222 Combine like terms: -14.72222222 + 14.72222222 = 0.00000000 0.00000000 + x = -23.689412646 + 14.72222222 x = -23.689412646 + 14.72222222 Combine like terms: -23.689412646 + 14.72222222 = -8.967190426 x = -8.967190426 Simplifying x = -8.967190426Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.411634866, -8.967190426}
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