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Simplifying 45x2 + -686x + 200 = 0 Reorder the terms: 200 + -686x + 45x2 = 0 Solving 200 + -686x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 4.444444444 + -15.24444444x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + -15.24444444x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + -15.24444444x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + -15.24444444x + x2 = 0 + -4.444444444 -15.24444444x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 -15.24444444x + x2 = -4.444444444 The x term is -15.24444444x. Take half its coefficient (-7.62222222). Square it (58.09827157) and add it to both sides. Add '58.09827157' to each side of the equation. -15.24444444x + 58.09827157 + x2 = -4.444444444 + 58.09827157 Reorder the terms: 58.09827157 + -15.24444444x + x2 = -4.444444444 + 58.09827157 Combine like terms: -4.444444444 + 58.09827157 = 53.653827126 58.09827157 + -15.24444444x + x2 = 53.653827126 Factor a perfect square on the left side: (x + -7.62222222)(x + -7.62222222) = 53.653827126 Calculate the square root of the right side: 7.324877277 Break this problem into two subproblems by setting (x + -7.62222222) equal to 7.324877277 and -7.324877277.Subproblem 1
x + -7.62222222 = 7.324877277 Simplifying x + -7.62222222 = 7.324877277 Reorder the terms: -7.62222222 + x = 7.324877277 Solving -7.62222222 + x = 7.324877277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.62222222' to each side of the equation. -7.62222222 + 7.62222222 + x = 7.324877277 + 7.62222222 Combine like terms: -7.62222222 + 7.62222222 = 0.00000000 0.00000000 + x = 7.324877277 + 7.62222222 x = 7.324877277 + 7.62222222 Combine like terms: 7.324877277 + 7.62222222 = 14.947099497 x = 14.947099497 Simplifying x = 14.947099497Subproblem 2
x + -7.62222222 = -7.324877277 Simplifying x + -7.62222222 = -7.324877277 Reorder the terms: -7.62222222 + x = -7.324877277 Solving -7.62222222 + x = -7.324877277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.62222222' to each side of the equation. -7.62222222 + 7.62222222 + x = -7.324877277 + 7.62222222 Combine like terms: -7.62222222 + 7.62222222 = 0.00000000 0.00000000 + x = -7.324877277 + 7.62222222 x = -7.324877277 + 7.62222222 Combine like terms: -7.324877277 + 7.62222222 = 0.297344943 x = 0.297344943 Simplifying x = 0.297344943Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.947099497, 0.297344943}
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