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Simplifying 81s2 + 72s = 16 Reorder the terms: 72s + 81s2 = 16 Solving 72s + 81s2 = 16 Solving for variable 's'. Reorder the terms: -16 + 72s + 81s2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 72s + 81s2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.1975308642 + 0.8888888889s + s2 = 0 Move the constant term to the right: Add '0.1975308642' to each side of the equation. -0.1975308642 + 0.8888888889s + 0.1975308642 + s2 = 0 + 0.1975308642 Reorder the terms: -0.1975308642 + 0.1975308642 + 0.8888888889s + s2 = 0 + 0.1975308642 Combine like terms: -0.1975308642 + 0.1975308642 = 0.0000000000 0.0000000000 + 0.8888888889s + s2 = 0 + 0.1975308642 0.8888888889s + s2 = 0 + 0.1975308642 Combine like terms: 0 + 0.1975308642 = 0.1975308642 0.8888888889s + s2 = 0.1975308642 The s term is 0.8888888889s. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889s + 0.1975308642 + s2 = 0.1975308642 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889s + s2 = 0.1975308642 + 0.1975308642 Combine like terms: 0.1975308642 + 0.1975308642 = 0.3950617284 0.1975308642 + 0.8888888889s + s2 = 0.3950617284 Factor a perfect square on the left side: (s + 0.4444444445)(s + 0.4444444445) = 0.3950617284 Calculate the square root of the right side: 0.628539361 Break this problem into two subproblems by setting (s + 0.4444444445) equal to 0.628539361 and -0.628539361.Subproblem 1
s + 0.4444444445 = 0.628539361 Simplifying s + 0.4444444445 = 0.628539361 Reorder the terms: 0.4444444445 + s = 0.628539361 Solving 0.4444444445 + s = 0.628539361 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + s = 0.628539361 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + s = 0.628539361 + -0.4444444445 s = 0.628539361 + -0.4444444445 Combine like terms: 0.628539361 + -0.4444444445 = 0.1840949165 s = 0.1840949165 Simplifying s = 0.1840949165Subproblem 2
s + 0.4444444445 = -0.628539361 Simplifying s + 0.4444444445 = -0.628539361 Reorder the terms: 0.4444444445 + s = -0.628539361 Solving 0.4444444445 + s = -0.628539361 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + s = -0.628539361 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + s = -0.628539361 + -0.4444444445 s = -0.628539361 + -0.4444444445 Combine like terms: -0.628539361 + -0.4444444445 = -1.0729838055 s = -1.0729838055 Simplifying s = -1.0729838055Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.1840949165, -1.0729838055}
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