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Simplifying 0.3x(x + 20) + -0.02(x + -60) = -9.6 Reorder the terms: 0.3x(20 + x) + -0.02(x + -60) = -9.6 (20 * 0.3x + x * 0.3x) + -0.02(x + -60) = -9.6 (6x + 0.3x2) + -0.02(x + -60) = -9.6 Reorder the terms: 6x + 0.3x2 + -0.02(-60 + x) = -9.6 6x + 0.3x2 + (-60 * -0.02 + x * -0.02) = -9.6 6x + 0.3x2 + (1.2 + -0.02x) = -9.6 Reorder the terms: 1.2 + 6x + -0.02x + 0.3x2 = -9.6 Combine like terms: 6x + -0.02x = 5.98x 1.2 + 5.98x + 0.3x2 = -9.6 Solving 1.2 + 5.98x + 0.3x2 = -9.6 Solving for variable 'x'. Reorder the terms: 1.2 + 9.6 + 5.98x + 0.3x2 = -9.6 + 9.6 Combine like terms: 1.2 + 9.6 = 10.8 10.8 + 5.98x + 0.3x2 = -9.6 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 10.8 + 5.98x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 36 + 19.93333333x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + 19.93333333x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 19.93333333x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 19.93333333x + x2 = 0 + -36 19.93333333x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 19.93333333x + x2 = -36 The x term is 19.93333333x. Take half its coefficient (9.966666665). Square it (99.33444441) and add it to both sides. Add '99.33444441' to each side of the equation. 19.93333333x + 99.33444441 + x2 = -36 + 99.33444441 Reorder the terms: 99.33444441 + 19.93333333x + x2 = -36 + 99.33444441 Combine like terms: -36 + 99.33444441 = 63.33444441 99.33444441 + 19.93333333x + x2 = 63.33444441 Factor a perfect square on the left side: (x + 9.966666665)(x + 9.966666665) = 63.33444441 Calculate the square root of the right side: 7.958294064 Break this problem into two subproblems by setting (x + 9.966666665) equal to 7.958294064 and -7.958294064.Subproblem 1
x + 9.966666665 = 7.958294064 Simplifying x + 9.966666665 = 7.958294064 Reorder the terms: 9.966666665 + x = 7.958294064 Solving 9.966666665 + x = 7.958294064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.966666665' to each side of the equation. 9.966666665 + -9.966666665 + x = 7.958294064 + -9.966666665 Combine like terms: 9.966666665 + -9.966666665 = 0.000000000 0.000000000 + x = 7.958294064 + -9.966666665 x = 7.958294064 + -9.966666665 Combine like terms: 7.958294064 + -9.966666665 = -2.008372601 x = -2.008372601 Simplifying x = -2.008372601Subproblem 2
x + 9.966666665 = -7.958294064 Simplifying x + 9.966666665 = -7.958294064 Reorder the terms: 9.966666665 + x = -7.958294064 Solving 9.966666665 + x = -7.958294064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.966666665' to each side of the equation. 9.966666665 + -9.966666665 + x = -7.958294064 + -9.966666665 Combine like terms: 9.966666665 + -9.966666665 = 0.000000000 0.000000000 + x = -7.958294064 + -9.966666665 x = -7.958294064 + -9.966666665 Combine like terms: -7.958294064 + -9.966666665 = -17.924960729 x = -17.924960729 Simplifying x = -17.924960729Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.008372601, -17.924960729}
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