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Simplifying 0 = -0.05x2 + 1.5x + 20 Reorder the terms: 0 = 20 + 1.5x + -0.05x2 Solving 0 = 20 + 1.5x + -0.05x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -1.5x + 0.05x2 = 20 + 1.5x + -0.05x2 + -20 + -1.5x + 0.05x2 Reorder the terms: -20 + -1.5x + 0.05x2 = 20 + -20 + 1.5x + -1.5x + -0.05x2 + 0.05x2 Combine like terms: 20 + -20 = 0 -20 + -1.5x + 0.05x2 = 0 + 1.5x + -1.5x + -0.05x2 + 0.05x2 -20 + -1.5x + 0.05x2 = 1.5x + -1.5x + -0.05x2 + 0.05x2 Combine like terms: 1.5x + -1.5x = 0.0 -20 + -1.5x + 0.05x2 = 0.0 + -0.05x2 + 0.05x2 -20 + -1.5x + 0.05x2 = -0.05x2 + 0.05x2 Combine like terms: -0.05x2 + 0.05x2 = 0.00 -20 + -1.5x + 0.05x2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -400 + -30x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -30x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -30x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -30x + x2 = 0 + 400 -30x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -30x + x2 = 400 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 = 400 + 225 Reorder the terms: 225 + -30x + x2 = 400 + 225 Combine like terms: 400 + 225 = 625 225 + -30x + x2 = 625 Factor a perfect square on the left side: (x + -15)(x + -15) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -15) equal to 25 and -25.Subproblem 1
x + -15 = 25 Simplifying x + -15 = 25 Reorder the terms: -15 + x = 25 Solving -15 + x = 25 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 = 25 + 15 Combine like terms: -15 + 15 = 0 0 + x = 25 + 15 x = 25 + 15 Combine like terms: 25 + 15 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -15 = -25 Simplifying x + -15 = -25 Reorder the terms: -15 + x = -25 Solving -15 + x = -25 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 = -25 + 15 Combine like terms: -15 + 15 = 0 0 + x = -25 + 15 x = -25 + 15 Combine like terms: -25 + 15 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -10}
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