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Simplifying 0.03x2 + -15x + 1600 = 0 Reorder the terms: 1600 + -15x + 0.03x2 = 0 Solving 1600 + -15x + 0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 53333.33333 + -500x + x2 = 0 Move the constant term to the right: Add '-53333.33333' to each side of the equation. 53333.33333 + -500x + -53333.33333 + x2 = 0 + -53333.33333 Reorder the terms: 53333.33333 + -53333.33333 + -500x + x2 = 0 + -53333.33333 Combine like terms: 53333.33333 + -53333.33333 = 0.00000 0.00000 + -500x + x2 = 0 + -53333.33333 -500x + x2 = 0 + -53333.33333 Combine like terms: 0 + -53333.33333 = -53333.33333 -500x + x2 = -53333.33333 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -53333.33333 + 62500 Reorder the terms: 62500 + -500x + x2 = -53333.33333 + 62500 Combine like terms: -53333.33333 + 62500 = 9166.66667 62500 + -500x + x2 = 9166.66667 Factor a perfect square on the left side: (x + -250)(x + -250) = 9166.66667 Calculate the square root of the right side: 95.742710793 Break this problem into two subproblems by setting (x + -250) equal to 95.742710793 and -95.742710793.Subproblem 1
x + -250 = 95.742710793 Simplifying x + -250 = 95.742710793 Reorder the terms: -250 + x = 95.742710793 Solving -250 + x = 95.742710793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 95.742710793 + 250 Combine like terms: -250 + 250 = 0 0 + x = 95.742710793 + 250 x = 95.742710793 + 250 Combine like terms: 95.742710793 + 250 = 345.742710793 x = 345.742710793 Simplifying x = 345.742710793Subproblem 2
x + -250 = -95.742710793 Simplifying x + -250 = -95.742710793 Reorder the terms: -250 + x = -95.742710793 Solving -250 + x = -95.742710793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -95.742710793 + 250 Combine like terms: -250 + 250 = 0 0 + x = -95.742710793 + 250 x = -95.742710793 + 250 Combine like terms: -95.742710793 + 250 = 154.257289207 x = 154.257289207 Simplifying x = 154.257289207Solution
The solution to the problem is based on the solutions from the subproblems. x = {345.742710793, 154.257289207}
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