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Simplifying 0.02x2 + -7x + 300 = 0 Reorder the terms: 300 + -7x + 0.02x2 = 0 Solving 300 + -7x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 15000 + -350x + x2 = 0 Move the constant term to the right: Add '-15000' to each side of the equation. 15000 + -350x + -15000 + x2 = 0 + -15000 Reorder the terms: 15000 + -15000 + -350x + x2 = 0 + -15000 Combine like terms: 15000 + -15000 = 0 0 + -350x + x2 = 0 + -15000 -350x + x2 = 0 + -15000 Combine like terms: 0 + -15000 = -15000 -350x + x2 = -15000 The x term is -350x. Take half its coefficient (-175). Square it (30625) and add it to both sides. Add '30625' to each side of the equation. -350x + 30625 + x2 = -15000 + 30625 Reorder the terms: 30625 + -350x + x2 = -15000 + 30625 Combine like terms: -15000 + 30625 = 15625 30625 + -350x + x2 = 15625 Factor a perfect square on the left side: (x + -175)(x + -175) = 15625 Calculate the square root of the right side: 125 Break this problem into two subproblems by setting (x + -175) equal to 125 and -125.Subproblem 1
x + -175 = 125 Simplifying x + -175 = 125 Reorder the terms: -175 + x = 125 Solving -175 + x = 125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = 125 + 175 Combine like terms: -175 + 175 = 0 0 + x = 125 + 175 x = 125 + 175 Combine like terms: 125 + 175 = 300 x = 300 Simplifying x = 300Subproblem 2
x + -175 = -125 Simplifying x + -175 = -125 Reorder the terms: -175 + x = -125 Solving -175 + x = -125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + x = -125 + 175 Combine like terms: -175 + 175 = 0 0 + x = -125 + 175 x = -125 + 175 Combine like terms: -125 + 175 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {300, 50}
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