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Simplifying (5s2) + 34s + 35 = 0 Reorder the terms: 35 + 34s + (5s2) = 0 Solving 35 + 34s + (5s2) = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7 + 6.8s + s2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6.8s + -7 + s2 = 0 + -7 Reorder the terms: 7 + -7 + 6.8s + s2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6.8s + s2 = 0 + -7 6.8s + s2 = 0 + -7 Combine like terms: 0 + -7 = -7 6.8s + s2 = -7 The s term is 6.8s. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8s + 11.56 + s2 = -7 + 11.56 Reorder the terms: 11.56 + 6.8s + s2 = -7 + 11.56 Combine like terms: -7 + 11.56 = 4.56 11.56 + 6.8s + s2 = 4.56 Factor a perfect square on the left side: ((s) + 3.4)((s) + 3.4) = 4.56 Calculate the square root of the right side: 2.13541565 Break this problem into two subproblems by setting ((s) + 3.4) equal to 2.13541565 and -2.13541565.Subproblem 1
(s) + 3.4 = 2.13541565 Simplifying (s) + 3.4 = 2.13541565 s + 3.4 = 2.13541565 Reorder the terms: 3.4 + s = 2.13541565 Solving 3.4 + s = 2.13541565 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + s = 2.13541565 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + s = 2.13541565 + -3.4 s = 2.13541565 + -3.4 Combine like terms: 2.13541565 + -3.4 = -1.26458435 s = -1.26458435 Simplifying s = -1.26458435Subproblem 2
(s) + 3.4 = -2.13541565 Simplifying (s) + 3.4 = -2.13541565 s + 3.4 = -2.13541565 Reorder the terms: 3.4 + s = -2.13541565 Solving 3.4 + s = -2.13541565 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + s = -2.13541565 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + s = -2.13541565 + -3.4 s = -2.13541565 + -3.4 Combine like terms: -2.13541565 + -3.4 = -5.53541565 s = -5.53541565 Simplifying s = -5.53541565Solution
The solution to the problem is based on the solutions from the subproblems. s = {-1.26458435, -5.53541565}
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