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Simplifying 99w2 + -9w + 8 = 999 Reorder the terms: 8 + -9w + 99w2 = 999 Solving 8 + -9w + 99w2 = 999 Solving for variable 'w'. Reorder the terms: 8 + -999 + -9w + 99w2 = 999 + -999 Combine like terms: 8 + -999 = -991 -991 + -9w + 99w2 = 999 + -999 Combine like terms: 999 + -999 = 0 -991 + -9w + 99w2 = 0 Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -10.01010101 + -0.09090909091w + w2 = 0 Move the constant term to the right: Add '10.01010101' to each side of the equation. -10.01010101 + -0.09090909091w + 10.01010101 + w2 = 0 + 10.01010101 Reorder the terms: -10.01010101 + 10.01010101 + -0.09090909091w + w2 = 0 + 10.01010101 Combine like terms: -10.01010101 + 10.01010101 = 0.00000000 0.00000000 + -0.09090909091w + w2 = 0 + 10.01010101 -0.09090909091w + w2 = 0 + 10.01010101 Combine like terms: 0 + 10.01010101 = 10.01010101 -0.09090909091w + w2 = 10.01010101 The w term is -0.09090909091w. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091w + 0.002066115703 + w2 = 10.01010101 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091w + w2 = 10.01010101 + 0.002066115703 Combine like terms: 10.01010101 + 0.002066115703 = 10.012167125703 0.002066115703 + -0.09090909091w + w2 = 10.012167125703 Factor a perfect square on the left side: (w + -0.04545454546)(w + -0.04545454546) = 10.012167125703 Calculate the square root of the right side: 3.164200867 Break this problem into two subproblems by setting (w + -0.04545454546) equal to 3.164200867 and -3.164200867.Subproblem 1
w + -0.04545454546 = 3.164200867 Simplifying w + -0.04545454546 = 3.164200867 Reorder the terms: -0.04545454546 + w = 3.164200867 Solving -0.04545454546 + w = 3.164200867 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + w = 3.164200867 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + w = 3.164200867 + 0.04545454546 w = 3.164200867 + 0.04545454546 Combine like terms: 3.164200867 + 0.04545454546 = 3.20965541246 w = 3.20965541246 Simplifying w = 3.20965541246Subproblem 2
w + -0.04545454546 = -3.164200867 Simplifying w + -0.04545454546 = -3.164200867 Reorder the terms: -0.04545454546 + w = -3.164200867 Solving -0.04545454546 + w = -3.164200867 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + w = -3.164200867 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + w = -3.164200867 + 0.04545454546 w = -3.164200867 + 0.04545454546 Combine like terms: -3.164200867 + 0.04545454546 = -3.11874632154 w = -3.11874632154 Simplifying w = -3.11874632154Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.20965541246, -3.11874632154}
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