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Simplifying 5w2 + 21w + -18 = 0 Reorder the terms: -18 + 21w + 5w2 = 0 Solving -18 + 21w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 4.2w + w2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 4.2w + 3.6 + w2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 4.2w + w2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 4.2w + w2 = 0 + 3.6 4.2w + w2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 4.2w + w2 = 3.6 The w term is 4.2w. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2w + 4.41 + w2 = 3.6 + 4.41 Reorder the terms: 4.41 + 4.2w + w2 = 3.6 + 4.41 Combine like terms: 3.6 + 4.41 = 8.01 4.41 + 4.2w + w2 = 8.01 Factor a perfect square on the left side: (w + 2.1)(w + 2.1) = 8.01 Calculate the square root of the right side: 2.83019434 Break this problem into two subproblems by setting (w + 2.1) equal to 2.83019434 and -2.83019434.Subproblem 1
w + 2.1 = 2.83019434 Simplifying w + 2.1 = 2.83019434 Reorder the terms: 2.1 + w = 2.83019434 Solving 2.1 + w = 2.83019434 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + w = 2.83019434 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + w = 2.83019434 + -2.1 w = 2.83019434 + -2.1 Combine like terms: 2.83019434 + -2.1 = 0.73019434 w = 0.73019434 Simplifying w = 0.73019434Subproblem 2
w + 2.1 = -2.83019434 Simplifying w + 2.1 = -2.83019434 Reorder the terms: 2.1 + w = -2.83019434 Solving 2.1 + w = -2.83019434 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + w = -2.83019434 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + w = -2.83019434 + -2.1 w = -2.83019434 + -2.1 Combine like terms: -2.83019434 + -2.1 = -4.93019434 w = -4.93019434 Simplifying w = -4.93019434Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.73019434, -4.93019434}
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