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Simplifying (-7w2 + -2w + -1) + -1(-5 + 3w + -2) = 0 Reorder the terms: (-1 + -2w + -7w2) + -1(-5 + 3w + -2) = 0 Remove parenthesis around (-1 + -2w + -7w2) -1 + -2w + -7w2 + -1(-5 + 3w + -2) = 0 Reorder the terms: -1 + -2w + -7w2 + -1(-5 + -2 + 3w) = 0 Combine like terms: -5 + -2 = -7 -1 + -2w + -7w2 + -1(-7 + 3w) = 0 -1 + -2w + -7w2 + (-7 * -1 + 3w * -1) = 0 -1 + -2w + -7w2 + (7 + -3w) = 0 Reorder the terms: -1 + 7 + -2w + -3w + -7w2 = 0 Combine like terms: -1 + 7 = 6 6 + -2w + -3w + -7w2 = 0 Combine like terms: -2w + -3w = -5w 6 + -5w + -7w2 = 0 Solving 6 + -5w + -7w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + 0.7142857143w + w2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.7142857143w + 0.8571428571 + w2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.7142857143w + w2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.7142857143w + w2 = 0 + 0.8571428571 0.7142857143w + w2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.7142857143w + w2 = 0.8571428571 The w term is 0.7142857143w. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143w + 0.1275510204 + w2 = 0.8571428571 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143w + w2 = 0.8571428571 + 0.1275510204 Combine like terms: 0.8571428571 + 0.1275510204 = 0.9846938775 0.1275510204 + 0.7142857143w + w2 = 0.9846938775 Factor a perfect square on the left side: (w + 0.3571428572)(w + 0.3571428572) = 0.9846938775 Calculate the square root of the right side: 0.992317428 Break this problem into two subproblems by setting (w + 0.3571428572) equal to 0.992317428 and -0.992317428.Subproblem 1
w + 0.3571428572 = 0.992317428 Simplifying w + 0.3571428572 = 0.992317428 Reorder the terms: 0.3571428572 + w = 0.992317428 Solving 0.3571428572 + w = 0.992317428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + w = 0.992317428 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + w = 0.992317428 + -0.3571428572 w = 0.992317428 + -0.3571428572 Combine like terms: 0.992317428 + -0.3571428572 = 0.6351745708 w = 0.6351745708 Simplifying w = 0.6351745708Subproblem 2
w + 0.3571428572 = -0.992317428 Simplifying w + 0.3571428572 = -0.992317428 Reorder the terms: 0.3571428572 + w = -0.992317428 Solving 0.3571428572 + w = -0.992317428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + w = -0.992317428 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + w = -0.992317428 + -0.3571428572 w = -0.992317428 + -0.3571428572 Combine like terms: -0.992317428 + -0.3571428572 = -1.3494602852 w = -1.3494602852 Simplifying w = -1.3494602852Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.6351745708, -1.3494602852}
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