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Simplifying 2x2 + 40x + 45 = 0 Reorder the terms: 45 + 40x + 2x2 = 0 Solving 45 + 40x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 20x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 20x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 20x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 20x + x2 = 0 + -22.5 20x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 20x + x2 = -22.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -22.5 + 100 Reorder the terms: 100 + 20x + x2 = -22.5 + 100 Combine like terms: -22.5 + 100 = 77.5 100 + 20x + x2 = 77.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 77.5 Calculate the square root of the right side: 8.803408431 Break this problem into two subproblems by setting (x + 10) equal to 8.803408431 and -8.803408431.Subproblem 1
x + 10 = 8.803408431 Simplifying x + 10 = 8.803408431 Reorder the terms: 10 + x = 8.803408431 Solving 10 + x = 8.803408431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 8.803408431 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.803408431 + -10 x = 8.803408431 + -10 Combine like terms: 8.803408431 + -10 = -1.196591569 x = -1.196591569 Simplifying x = -1.196591569Subproblem 2
x + 10 = -8.803408431 Simplifying x + 10 = -8.803408431 Reorder the terms: 10 + x = -8.803408431 Solving 10 + x = -8.803408431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -8.803408431 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.803408431 + -10 x = -8.803408431 + -10 Combine like terms: -8.803408431 + -10 = -18.803408431 x = -18.803408431 Simplifying x = -18.803408431Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.196591569, -18.803408431}
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