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Simplifying -0.1x2 + 20x + -750 = 0 Reorder the terms: -750 + 20x + -0.1x2 = 0 Solving -750 + 20x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 7500 + -200x + x2 = 0 Move the constant term to the right: Add '-7500' to each side of the equation. 7500 + -200x + -7500 + x2 = 0 + -7500 Reorder the terms: 7500 + -7500 + -200x + x2 = 0 + -7500 Combine like terms: 7500 + -7500 = 0 0 + -200x + x2 = 0 + -7500 -200x + x2 = 0 + -7500 Combine like terms: 0 + -7500 = -7500 -200x + x2 = -7500 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -7500 + 10000 Reorder the terms: 10000 + -200x + x2 = -7500 + 10000 Combine like terms: -7500 + 10000 = 2500 10000 + -200x + x2 = 2500 Factor a perfect square on the left side: (x + -100)(x + -100) = 2500 Calculate the square root of the right side: 50 Break this problem into two subproblems by setting (x + -100) equal to 50 and -50.Subproblem 1
x + -100 = 50 Simplifying x + -100 = 50 Reorder the terms: -100 + x = 50 Solving -100 + x = 50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 50 + 100 Combine like terms: -100 + 100 = 0 0 + x = 50 + 100 x = 50 + 100 Combine like terms: 50 + 100 = 150 x = 150 Simplifying x = 150Subproblem 2
x + -100 = -50 Simplifying x + -100 = -50 Reorder the terms: -100 + x = -50 Solving -100 + x = -50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -50 + 100 Combine like terms: -100 + 100 = 0 0 + x = -50 + 100 x = -50 + 100 Combine like terms: -50 + 100 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {150, 50}
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