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Simplifying 361x2 + 60x + 2 = 0 Reorder the terms: 2 + 60x + 361x2 = 0 Solving 2 + 60x + 361x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 361 the coefficient of the squared term: Divide each side by '361'. 0.005540166205 + 0.1662049861x + x2 = 0 Move the constant term to the right: Add '-0.005540166205' to each side of the equation. 0.005540166205 + 0.1662049861x + -0.005540166205 + x2 = 0 + -0.005540166205 Reorder the terms: 0.005540166205 + -0.005540166205 + 0.1662049861x + x2 = 0 + -0.005540166205 Combine like terms: 0.005540166205 + -0.005540166205 = 0.000000000000 0.000000000000 + 0.1662049861x + x2 = 0 + -0.005540166205 0.1662049861x + x2 = 0 + -0.005540166205 Combine like terms: 0 + -0.005540166205 = -0.005540166205 0.1662049861x + x2 = -0.005540166205 The x term is 0.1662049861x. Take half its coefficient (0.08310249305). Square it (0.006906024351) and add it to both sides. Add '0.006906024351' to each side of the equation. 0.1662049861x + 0.006906024351 + x2 = -0.005540166205 + 0.006906024351 Reorder the terms: 0.006906024351 + 0.1662049861x + x2 = -0.005540166205 + 0.006906024351 Combine like terms: -0.005540166205 + 0.006906024351 = 0.001365858146 0.006906024351 + 0.1662049861x + x2 = 0.001365858146 Factor a perfect square on the left side: (x + 0.08310249305)(x + 0.08310249305) = 0.001365858146 Calculate the square root of the right side: 0.036957518 Break this problem into two subproblems by setting (x + 0.08310249305) equal to 0.036957518 and -0.036957518.Subproblem 1
x + 0.08310249305 = 0.036957518 Simplifying x + 0.08310249305 = 0.036957518 Reorder the terms: 0.08310249305 + x = 0.036957518 Solving 0.08310249305 + x = 0.036957518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08310249305' to each side of the equation. 0.08310249305 + -0.08310249305 + x = 0.036957518 + -0.08310249305 Combine like terms: 0.08310249305 + -0.08310249305 = 0.00000000000 0.00000000000 + x = 0.036957518 + -0.08310249305 x = 0.036957518 + -0.08310249305 Combine like terms: 0.036957518 + -0.08310249305 = -0.04614497505 x = -0.04614497505 Simplifying x = -0.04614497505Subproblem 2
x + 0.08310249305 = -0.036957518 Simplifying x + 0.08310249305 = -0.036957518 Reorder the terms: 0.08310249305 + x = -0.036957518 Solving 0.08310249305 + x = -0.036957518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08310249305' to each side of the equation. 0.08310249305 + -0.08310249305 + x = -0.036957518 + -0.08310249305 Combine like terms: 0.08310249305 + -0.08310249305 = 0.00000000000 0.00000000000 + x = -0.036957518 + -0.08310249305 x = -0.036957518 + -0.08310249305 Combine like terms: -0.036957518 + -0.08310249305 = -0.12006001105 x = -0.12006001105 Simplifying x = -0.12006001105Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.04614497505, -0.12006001105}
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