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Simplifying 10w2 + -3w + -77 = 0 Reorder the terms: -77 + -3w + 10w2 = 0 Solving -77 + -3w + 10w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -7.7 + -0.3w + w2 = 0 Move the constant term to the right: Add '7.7' to each side of the equation. -7.7 + -0.3w + 7.7 + w2 = 0 + 7.7 Reorder the terms: -7.7 + 7.7 + -0.3w + w2 = 0 + 7.7 Combine like terms: -7.7 + 7.7 = 0.0 0.0 + -0.3w + w2 = 0 + 7.7 -0.3w + w2 = 0 + 7.7 Combine like terms: 0 + 7.7 = 7.7 -0.3w + w2 = 7.7 The w term is -0.3w. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3w + 0.0225 + w2 = 7.7 + 0.0225 Reorder the terms: 0.0225 + -0.3w + w2 = 7.7 + 0.0225 Combine like terms: 7.7 + 0.0225 = 7.7225 0.0225 + -0.3w + w2 = 7.7225 Factor a perfect square on the left side: (w + -0.15)(w + -0.15) = 7.7225 Calculate the square root of the right side: 2.778938646 Break this problem into two subproblems by setting (w + -0.15) equal to 2.778938646 and -2.778938646.Subproblem 1
w + -0.15 = 2.778938646 Simplifying w + -0.15 = 2.778938646 Reorder the terms: -0.15 + w = 2.778938646 Solving -0.15 + w = 2.778938646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + w = 2.778938646 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + w = 2.778938646 + 0.15 w = 2.778938646 + 0.15 Combine like terms: 2.778938646 + 0.15 = 2.928938646 w = 2.928938646 Simplifying w = 2.928938646Subproblem 2
w + -0.15 = -2.778938646 Simplifying w + -0.15 = -2.778938646 Reorder the terms: -0.15 + w = -2.778938646 Solving -0.15 + w = -2.778938646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + w = -2.778938646 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + w = -2.778938646 + 0.15 w = -2.778938646 + 0.15 Combine like terms: -2.778938646 + 0.15 = -2.628938646 w = -2.628938646 Simplifying w = -2.628938646Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.928938646, -2.628938646}
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