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Simplifying 5w2 + 2w + -42 = 0 Reorder the terms: -42 + 2w + 5w2 = 0 Solving -42 + 2w + 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'. -8.4 + 0.4w + w2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + 0.4w + 8.4 + w2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + 0.4w + w2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + 0.4w + w2 = 0 + 8.4 0.4w + w2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 0.4w + w2 = 8.4 The w term is 0.4w. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4w + 0.04 + w2 = 8.4 + 0.04 Reorder the terms: 0.04 + 0.4w + w2 = 8.4 + 0.04 Combine like terms: 8.4 + 0.04 = 8.44 0.04 + 0.4w + w2 = 8.44 Factor a perfect square on the left side: (w + 0.2)(w + 0.2) = 8.44 Calculate the square root of the right side: 2.905167809 Break this problem into two subproblems by setting (w + 0.2) equal to 2.905167809 and -2.905167809.Subproblem 1
w + 0.2 = 2.905167809 Simplifying w + 0.2 = 2.905167809 Reorder the terms: 0.2 + w = 2.905167809 Solving 0.2 + w = 2.905167809 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + w = 2.905167809 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = 2.905167809 + -0.2 w = 2.905167809 + -0.2 Combine like terms: 2.905167809 + -0.2 = 2.705167809 w = 2.705167809 Simplifying w = 2.705167809Subproblem 2
w + 0.2 = -2.905167809 Simplifying w + 0.2 = -2.905167809 Reorder the terms: 0.2 + w = -2.905167809 Solving 0.2 + w = -2.905167809 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + w = -2.905167809 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = -2.905167809 + -0.2 w = -2.905167809 + -0.2 Combine like terms: -2.905167809 + -0.2 = -3.105167809 w = -3.105167809 Simplifying w = -3.105167809Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.705167809, -3.105167809}
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