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Simplifying 0.05x2 + 10x + 600 = 25x Reorder the terms: 600 + 10x + 0.05x2 = 25x Solving 600 + 10x + 0.05x2 = 25x Solving for variable 'x'. Reorder the terms: 600 + 10x + -25x + 0.05x2 = 25x + -25x Combine like terms: 10x + -25x = -15x 600 + -15x + 0.05x2 = 25x + -25x Combine like terms: 25x + -25x = 0 600 + -15x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 12000 + -300x + x2 = 0 Move the constant term to the right: Add '-12000' to each side of the equation. 12000 + -300x + -12000 + x2 = 0 + -12000 Reorder the terms: 12000 + -12000 + -300x + x2 = 0 + -12000 Combine like terms: 12000 + -12000 = 0 0 + -300x + x2 = 0 + -12000 -300x + x2 = 0 + -12000 Combine like terms: 0 + -12000 = -12000 -300x + x2 = -12000 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -12000 + 22500 Reorder the terms: 22500 + -300x + x2 = -12000 + 22500 Combine like terms: -12000 + 22500 = 10500 22500 + -300x + x2 = 10500 Factor a perfect square on the left side: (x + -150)(x + -150) = 10500 Calculate the square root of the right side: 102.46950766 Break this problem into two subproblems by setting (x + -150) equal to 102.46950766 and -102.46950766.Subproblem 1
x + -150 = 102.46950766 Simplifying x + -150 = 102.46950766 Reorder the terms: -150 + x = 102.46950766 Solving -150 + x = 102.46950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 102.46950766 + 150 Combine like terms: -150 + 150 = 0 0 + x = 102.46950766 + 150 x = 102.46950766 + 150 Combine like terms: 102.46950766 + 150 = 252.46950766 x = 252.46950766 Simplifying x = 252.46950766Subproblem 2
x + -150 = -102.46950766 Simplifying x + -150 = -102.46950766 Reorder the terms: -150 + x = -102.46950766 Solving -150 + x = -102.46950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -102.46950766 + 150 Combine like terms: -150 + 150 = 0 0 + x = -102.46950766 + 150 x = -102.46950766 + 150 Combine like terms: -102.46950766 + 150 = 47.53049234 x = 47.53049234 Simplifying x = 47.53049234Solution
The solution to the problem is based on the solutions from the subproblems. x = {252.46950766, 47.53049234}
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