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Simplifying (5w)(5w) + -3w + -17 = 0 Remove parenthesis around (5w) 5w(5w) + -3w + -17 = 0 Remove parenthesis around (5w) 5w * 5w + -3w + -17 = 0 Reorder the terms for easier multiplication: 5 * 5w * w + -3w + -17 = 0 Multiply 5 * 5 25w * w + -3w + -17 = 0 Multiply w * w 25w2 + -3w + -17 = 0 Reorder the terms: -17 + -3w + 25w2 = 0 Solving -17 + -3w + 25w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.68 + -0.12w + w2 = 0 Move the constant term to the right: Add '0.68' to each side of the equation. -0.68 + -0.12w + 0.68 + w2 = 0 + 0.68 Reorder the terms: -0.68 + 0.68 + -0.12w + w2 = 0 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + -0.12w + w2 = 0 + 0.68 -0.12w + w2 = 0 + 0.68 Combine like terms: 0 + 0.68 = 0.68 -0.12w + w2 = 0.68 The w term is -0.12w. Take half its coefficient (-0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. -0.12w + 0.0036 + w2 = 0.68 + 0.0036 Reorder the terms: 0.0036 + -0.12w + w2 = 0.68 + 0.0036 Combine like terms: 0.68 + 0.0036 = 0.6836 0.0036 + -0.12w + w2 = 0.6836 Factor a perfect square on the left side: (w + -0.06)(w + -0.06) = 0.6836 Calculate the square root of the right side: 0.826801064 Break this problem into two subproblems by setting (w + -0.06) equal to 0.826801064 and -0.826801064.Subproblem 1
w + -0.06 = 0.826801064 Simplifying w + -0.06 = 0.826801064 Reorder the terms: -0.06 + w = 0.826801064 Solving -0.06 + w = 0.826801064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + w = 0.826801064 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + w = 0.826801064 + 0.06 w = 0.826801064 + 0.06 Combine like terms: 0.826801064 + 0.06 = 0.886801064 w = 0.886801064 Simplifying w = 0.886801064Subproblem 2
w + -0.06 = -0.826801064 Simplifying w + -0.06 = -0.826801064 Reorder the terms: -0.06 + w = -0.826801064 Solving -0.06 + w = -0.826801064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.06' to each side of the equation. -0.06 + 0.06 + w = -0.826801064 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + w = -0.826801064 + 0.06 w = -0.826801064 + 0.06 Combine like terms: -0.826801064 + 0.06 = -0.766801064 w = -0.766801064 Simplifying w = -0.766801064Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.886801064, -0.766801064}
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