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Simplifying 3s2 + 320s + -1960 = 0 Reorder the terms: -1960 + 320s + 3s2 = 0 Solving -1960 + 320s + 3s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -653.3333333 + 106.6666667s + s2 = 0 Move the constant term to the right: Add '653.3333333' to each side of the equation. -653.3333333 + 106.6666667s + 653.3333333 + s2 = 0 + 653.3333333 Reorder the terms: -653.3333333 + 653.3333333 + 106.6666667s + s2 = 0 + 653.3333333 Combine like terms: -653.3333333 + 653.3333333 = 0.0000000 0.0000000 + 106.6666667s + s2 = 0 + 653.3333333 106.6666667s + s2 = 0 + 653.3333333 Combine like terms: 0 + 653.3333333 = 653.3333333 106.6666667s + s2 = 653.3333333 The s term is 106.6666667s. Take half its coefficient (53.33333335). Square it (2844.444446) and add it to both sides. Add '2844.444446' to each side of the equation. 106.6666667s + 2844.444446 + s2 = 653.3333333 + 2844.444446 Reorder the terms: 2844.444446 + 106.6666667s + s2 = 653.3333333 + 2844.444446 Combine like terms: 653.3333333 + 2844.444446 = 3497.7777793 2844.444446 + 106.6666667s + s2 = 3497.7777793 Factor a perfect square on the left side: (s + 53.33333335)(s + 53.33333335) = 3497.7777793 Calculate the square root of the right side: 59.142013656 Break this problem into two subproblems by setting (s + 53.33333335) equal to 59.142013656 and -59.142013656.Subproblem 1
s + 53.33333335 = 59.142013656 Simplifying s + 53.33333335 = 59.142013656 Reorder the terms: 53.33333335 + s = 59.142013656 Solving 53.33333335 + s = 59.142013656 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-53.33333335' to each side of the equation. 53.33333335 + -53.33333335 + s = 59.142013656 + -53.33333335 Combine like terms: 53.33333335 + -53.33333335 = 0.00000000 0.00000000 + s = 59.142013656 + -53.33333335 s = 59.142013656 + -53.33333335 Combine like terms: 59.142013656 + -53.33333335 = 5.808680306 s = 5.808680306 Simplifying s = 5.808680306Subproblem 2
s + 53.33333335 = -59.142013656 Simplifying s + 53.33333335 = -59.142013656 Reorder the terms: 53.33333335 + s = -59.142013656 Solving 53.33333335 + s = -59.142013656 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-53.33333335' to each side of the equation. 53.33333335 + -53.33333335 + s = -59.142013656 + -53.33333335 Combine like terms: 53.33333335 + -53.33333335 = 0.00000000 0.00000000 + s = -59.142013656 + -53.33333335 s = -59.142013656 + -53.33333335 Combine like terms: -59.142013656 + -53.33333335 = -112.475347006 s = -112.475347006 Simplifying s = -112.475347006Solution
The solution to the problem is based on the solutions from the subproblems. s = {5.808680306, -112.475347006}
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