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Simplifying 0.05x2 + -1.5x + 10 = 0 Reorder the terms: 10 + -1.5x + 0.05x2 = 0 Solving 10 + -1.5x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 200 + -30x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -30x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -30x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -30x + x2 = 0 + -200 -30x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -30x + x2 = -200 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -200 + 225 Reorder the terms: 225 + -30x + x2 = -200 + 225 Combine like terms: -200 + 225 = 25 225 + -30x + x2 = 25 Factor a perfect square on the left side: (x + -15)(x + -15) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -15) equal to 5 and -5.Subproblem 1
x + -15 = 5 Simplifying x + -15 = 5 Reorder the terms: -15 + x = 5 Solving -15 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 5 + 15 Combine like terms: -15 + 15 = 0 0 + x = 5 + 15 x = 5 + 15 Combine like terms: 5 + 15 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -15 = -5 Simplifying x + -15 = -5 Reorder the terms: -15 + x = -5 Solving -15 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -5 + 15 Combine like terms: -15 + 15 = 0 0 + x = -5 + 15 x = -5 + 15 Combine like terms: -5 + 15 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, 10}
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