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Simplifying w2 + 0.13w + -0.051 = 0 Reorder the terms: -0.051 + 0.13w + w2 = 0 Solving -0.051 + 0.13w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '0.051' to each side of the equation. -0.051 + 0.13w + 0.051 + w2 = 0 + 0.051 Reorder the terms: -0.051 + 0.051 + 0.13w + w2 = 0 + 0.051 Combine like terms: -0.051 + 0.051 = 0.000 0.000 + 0.13w + w2 = 0 + 0.051 0.13w + w2 = 0 + 0.051 Combine like terms: 0 + 0.051 = 0.051 0.13w + w2 = 0.051 The w term is 0.13w. Take half its coefficient (0.065). Square it (0.004225) and add it to both sides. Add '0.004225' to each side of the equation. 0.13w + 0.004225 + w2 = 0.051 + 0.004225 Reorder the terms: 0.004225 + 0.13w + w2 = 0.051 + 0.004225 Combine like terms: 0.051 + 0.004225 = 0.055225 0.004225 + 0.13w + w2 = 0.055225 Factor a perfect square on the left side: (w + 0.065)(w + 0.065) = 0.055225 Calculate the square root of the right side: 0.235 Break this problem into two subproblems by setting (w + 0.065) equal to 0.235 and -0.235.Subproblem 1
w + 0.065 = 0.235 Simplifying w + 0.065 = 0.235 Reorder the terms: 0.065 + w = 0.235 Solving 0.065 + w = 0.235 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.065' to each side of the equation. 0.065 + -0.065 + w = 0.235 + -0.065 Combine like terms: 0.065 + -0.065 = 0.000 0.000 + w = 0.235 + -0.065 w = 0.235 + -0.065 Combine like terms: 0.235 + -0.065 = 0.17 w = 0.17 Simplifying w = 0.17Subproblem 2
w + 0.065 = -0.235 Simplifying w + 0.065 = -0.235 Reorder the terms: 0.065 + w = -0.235 Solving 0.065 + w = -0.235 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.065' to each side of the equation. 0.065 + -0.065 + w = -0.235 + -0.065 Combine like terms: 0.065 + -0.065 = 0.000 0.000 + w = -0.235 + -0.065 w = -0.235 + -0.065 Combine like terms: -0.235 + -0.065 = -0.3 w = -0.3 Simplifying w = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.17, -0.3}
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