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Simplifying 0 = -0.03x2 + 1.8x + -25 Reorder the terms: 0 = -25 + 1.8x + -0.03x2 Solving 0 = -25 + 1.8x + -0.03x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -1.8x + 0.03x2 = -25 + 1.8x + -0.03x2 + 25 + -1.8x + 0.03x2 Reorder the terms: 25 + -1.8x + 0.03x2 = -25 + 25 + 1.8x + -1.8x + -0.03x2 + 0.03x2 Combine like terms: -25 + 25 = 0 25 + -1.8x + 0.03x2 = 0 + 1.8x + -1.8x + -0.03x2 + 0.03x2 25 + -1.8x + 0.03x2 = 1.8x + -1.8x + -0.03x2 + 0.03x2 Combine like terms: 1.8x + -1.8x = 0.0 25 + -1.8x + 0.03x2 = 0.0 + -0.03x2 + 0.03x2 25 + -1.8x + 0.03x2 = -0.03x2 + 0.03x2 Combine like terms: -0.03x2 + 0.03x2 = 0.00 25 + -1.8x + 0.03x2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 833.3333333 + -60x + x2 = 0 Move the constant term to the right: Add '-833.3333333' to each side of the equation. 833.3333333 + -60x + -833.3333333 + x2 = 0 + -833.3333333 Reorder the terms: 833.3333333 + -833.3333333 + -60x + x2 = 0 + -833.3333333 Combine like terms: 833.3333333 + -833.3333333 = 0.0000000 0.0000000 + -60x + x2 = 0 + -833.3333333 -60x + x2 = 0 + -833.3333333 Combine like terms: 0 + -833.3333333 = -833.3333333 -60x + x2 = -833.3333333 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 = -833.3333333 + 900 Reorder the terms: 900 + -60x + x2 = -833.3333333 + 900 Combine like terms: -833.3333333 + 900 = 66.6666667 900 + -60x + x2 = 66.6666667 Factor a perfect square on the left side: (x + -30)(x + -30) = 66.6666667 Calculate the square root of the right side: 8.164965811 Break this problem into two subproblems by setting (x + -30) equal to 8.164965811 and -8.164965811.Subproblem 1
x + -30 = 8.164965811 Simplifying x + -30 = 8.164965811 Reorder the terms: -30 + x = 8.164965811 Solving -30 + x = 8.164965811 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 = 8.164965811 + 30 Combine like terms: -30 + 30 = 0 0 + x = 8.164965811 + 30 x = 8.164965811 + 30 Combine like terms: 8.164965811 + 30 = 38.164965811 x = 38.164965811 Simplifying x = 38.164965811Subproblem 2
x + -30 = -8.164965811 Simplifying x + -30 = -8.164965811 Reorder the terms: -30 + x = -8.164965811 Solving -30 + x = -8.164965811 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 = -8.164965811 + 30 Combine like terms: -30 + 30 = 0 0 + x = -8.164965811 + 30 x = -8.164965811 + 30 Combine like terms: -8.164965811 + 30 = 21.835034189 x = 21.835034189 Simplifying x = 21.835034189Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.164965811, 21.835034189}
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