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Simplifying 10 = -0.02x2 + 1.2x Reorder the terms: 10 = 1.2x + -0.02x2 Solving 10 = 1.2x + -0.02x2 Solving for variable 'x'. Reorder the terms: 10 + -1.2x + 0.02x2 = 1.2x + -1.2x + -0.02x2 + 0.02x2 Combine like terms: 1.2x + -1.2x = 0.0 10 + -1.2x + 0.02x2 = 0.0 + -0.02x2 + 0.02x2 10 + -1.2x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 10 + -1.2x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 500 + -60x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -60x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -60x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -60x + x2 = 0 + -500 -60x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -60x + x2 = -500 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 = -500 + 900 Reorder the terms: 900 + -60x + x2 = -500 + 900 Combine like terms: -500 + 900 = 400 900 + -60x + x2 = 400 Factor a perfect square on the left side: (x + -30)(x + -30) = 400 Calculate the square root of the right side: 20 Break this problem into two subproblems by setting (x + -30) equal to 20 and -20.Subproblem 1
x + -30 = 20 Simplifying x + -30 = 20 Reorder the terms: -30 + x = 20 Solving -30 + x = 20 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 = 20 + 30 Combine like terms: -30 + 30 = 0 0 + x = 20 + 30 x = 20 + 30 Combine like terms: 20 + 30 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -30 = -20 Simplifying x + -30 = -20 Reorder the terms: -30 + x = -20 Solving -30 + x = -20 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 = -20 + 30 Combine like terms: -30 + 30 = 0 0 + x = -20 + 30 x = -20 + 30 Combine like terms: -20 + 30 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, 10}
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