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Simplifying 80 = 6x + -0.1x2 Solving 80 = 6x + -0.1x2 Solving for variable 'x'. Reorder the terms: 80 + -6x + 0.1x2 = 6x + -6x + -0.1x2 + 0.1x2 Combine like terms: 6x + -6x = 0 80 + -6x + 0.1x2 = 0 + -0.1x2 + 0.1x2 80 + -6x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 80 + -6x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 800 + -60x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -60x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -60x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -60x + x2 = 0 + -800 -60x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -60x + x2 = -800 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -800 + 900 Reorder the terms: 900 + -60x + x2 = -800 + 900 Combine like terms: -800 + 900 = 100 900 + -60x + x2 = 100 Factor a perfect square on the left side: (x + -30)(x + -30) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -30) equal to 10 and -10.Subproblem 1
x + -30 = 10 Simplifying x + -30 = 10 Reorder the terms: -30 + x = 10 Solving -30 + x = 10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 10 + 30 Combine like terms: -30 + 30 = 0 0 + x = 10 + 30 x = 10 + 30 Combine like terms: 10 + 30 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -30 = -10 Simplifying x + -30 = -10 Reorder the terms: -30 + x = -10 Solving -30 + x = -10 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -10 + 30 Combine like terms: -30 + 30 = 0 0 + x = -10 + 30 x = -10 + 30 Combine like terms: -10 + 30 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, 20}
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