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Simplifying 9w2 + -15w + -28 = 0 Reorder the terms: -28 + -15w + 9w2 = 0 Solving -28 + -15w + 9w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + -1.666666667w + w2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + -1.666666667w + 3.111111111 + w2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + -1.666666667w + w2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + -1.666666667w + w2 = 0 + 3.111111111 -1.666666667w + w2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 -1.666666667w + w2 = 3.111111111 The w term is -1.666666667w. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667w + 0.6944444447 + w2 = 3.111111111 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667w + w2 = 3.111111111 + 0.6944444447 Combine like terms: 3.111111111 + 0.6944444447 = 3.8055555557 0.6944444447 + -1.666666667w + w2 = 3.8055555557 Factor a perfect square on the left side: (w + -0.8333333335)(w + -0.8333333335) = 3.8055555557 Calculate the square root of the right side: 1.950783318 Break this problem into two subproblems by setting (w + -0.8333333335) equal to 1.950783318 and -1.950783318.Subproblem 1
w + -0.8333333335 = 1.950783318 Simplifying w + -0.8333333335 = 1.950783318 Reorder the terms: -0.8333333335 + w = 1.950783318 Solving -0.8333333335 + w = 1.950783318 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = 1.950783318 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = 1.950783318 + 0.8333333335 w = 1.950783318 + 0.8333333335 Combine like terms: 1.950783318 + 0.8333333335 = 2.7841166515 w = 2.7841166515 Simplifying w = 2.7841166515Subproblem 2
w + -0.8333333335 = -1.950783318 Simplifying w + -0.8333333335 = -1.950783318 Reorder the terms: -0.8333333335 + w = -1.950783318 Solving -0.8333333335 + w = -1.950783318 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + w = -1.950783318 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + w = -1.950783318 + 0.8333333335 w = -1.950783318 + 0.8333333335 Combine like terms: -1.950783318 + 0.8333333335 = -1.1174499845 w = -1.1174499845 Simplifying w = -1.1174499845Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.7841166515, -1.1174499845}
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