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Simplifying 199 = 0.1w2 + 2.155w + 19.985 Reorder the terms: 199 = 19.985 + 2.155w + 0.1w2 Solving 199 = 19.985 + 2.155w + 0.1w2 Solving for variable 'w'. Combine like terms: 199 + -19.985 = 179.015 179.015 + -2.155w + -0.1w2 = 19.985 + 2.155w + 0.1w2 + -19.985 + -2.155w + -0.1w2 Reorder the terms: 179.015 + -2.155w + -0.1w2 = 19.985 + -19.985 + 2.155w + -2.155w + 0.1w2 + -0.1w2 Combine like terms: 19.985 + -19.985 = 0.000 179.015 + -2.155w + -0.1w2 = 0.000 + 2.155w + -2.155w + 0.1w2 + -0.1w2 179.015 + -2.155w + -0.1w2 = 2.155w + -2.155w + 0.1w2 + -0.1w2 Combine like terms: 2.155w + -2.155w = 0.000 179.015 + -2.155w + -0.1w2 = 0.000 + 0.1w2 + -0.1w2 179.015 + -2.155w + -0.1w2 = 0.1w2 + -0.1w2 Combine like terms: 0.1w2 + -0.1w2 = 0.0 179.015 + -2.155w + -0.1w2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -1790.15 + 21.55w + w2 = 0 Move the constant term to the right: Add '1790.15' to each side of the equation. -1790.15 + 21.55w + 1790.15 + w2 = 0 + 1790.15 Reorder the terms: -1790.15 + 1790.15 + 21.55w + w2 = 0 + 1790.15 Combine like terms: -1790.15 + 1790.15 = 0.00 0.00 + 21.55w + w2 = 0 + 1790.15 21.55w + w2 = 0 + 1790.15 Combine like terms: 0 + 1790.15 = 1790.15 21.55w + w2 = 1790.15 The w term is 21.55w. Take half its coefficient (10.775). Square it (116.100625) and add it to both sides. Add '116.100625' to each side of the equation. 21.55w + 116.100625 + w2 = 1790.15 + 116.100625 Reorder the terms: 116.100625 + 21.55w + w2 = 1790.15 + 116.100625 Combine like terms: 1790.15 + 116.100625 = 1906.250625 116.100625 + 21.55w + w2 = 1906.250625 Factor a perfect square on the left side: (w + 10.775)(w + 10.775) = 1906.250625 Calculate the square root of the right side: 43.660630149 Break this problem into two subproblems by setting (w + 10.775) equal to 43.660630149 and -43.660630149.Subproblem 1
w + 10.775 = 43.660630149 Simplifying w + 10.775 = 43.660630149 Reorder the terms: 10.775 + w = 43.660630149 Solving 10.775 + w = 43.660630149 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10.775' to each side of the equation. 10.775 + -10.775 + w = 43.660630149 + -10.775 Combine like terms: 10.775 + -10.775 = 0.000 0.000 + w = 43.660630149 + -10.775 w = 43.660630149 + -10.775 Combine like terms: 43.660630149 + -10.775 = 32.885630149 w = 32.885630149 Simplifying w = 32.885630149Subproblem 2
w + 10.775 = -43.660630149 Simplifying w + 10.775 = -43.660630149 Reorder the terms: 10.775 + w = -43.660630149 Solving 10.775 + w = -43.660630149 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10.775' to each side of the equation. 10.775 + -10.775 + w = -43.660630149 + -10.775 Combine like terms: 10.775 + -10.775 = 0.000 0.000 + w = -43.660630149 + -10.775 w = -43.660630149 + -10.775 Combine like terms: -43.660630149 + -10.775 = -54.435630149 w = -54.435630149 Simplifying w = -54.435630149Solution
The solution to the problem is based on the solutions from the subproblems. w = {32.885630149, -54.435630149}
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