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Simplifying 81s2 + 126s = 49 Reorder the terms: 126s + 81s2 = 49 Solving 126s + 81s2 = 49 Solving for variable 's'. Reorder the terms: -49 + 126s + 81s2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 126s + 81s2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.6049382716 + 1.555555556s + s2 = 0 Move the constant term to the right: Add '0.6049382716' to each side of the equation. -0.6049382716 + 1.555555556s + 0.6049382716 + s2 = 0 + 0.6049382716 Reorder the terms: -0.6049382716 + 0.6049382716 + 1.555555556s + s2 = 0 + 0.6049382716 Combine like terms: -0.6049382716 + 0.6049382716 = 0.0000000000 0.0000000000 + 1.555555556s + s2 = 0 + 0.6049382716 1.555555556s + s2 = 0 + 0.6049382716 Combine like terms: 0 + 0.6049382716 = 0.6049382716 1.555555556s + s2 = 0.6049382716 The s term is 1.555555556s. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556s + 0.6049382720 + s2 = 0.6049382716 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556s + s2 = 0.6049382716 + 0.6049382720 Combine like terms: 0.6049382716 + 0.6049382720 = 1.2098765436 0.6049382720 + 1.555555556s + s2 = 1.2098765436 Factor a perfect square on the left side: (s + 0.777777778)(s + 0.777777778) = 1.2098765436 Calculate the square root of the right side: 1.099943882 Break this problem into two subproblems by setting (s + 0.777777778) equal to 1.099943882 and -1.099943882.Subproblem 1
s + 0.777777778 = 1.099943882 Simplifying s + 0.777777778 = 1.099943882 Reorder the terms: 0.777777778 + s = 1.099943882 Solving 0.777777778 + s = 1.099943882 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + s = 1.099943882 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + s = 1.099943882 + -0.777777778 s = 1.099943882 + -0.777777778 Combine like terms: 1.099943882 + -0.777777778 = 0.322166104 s = 0.322166104 Simplifying s = 0.322166104Subproblem 2
s + 0.777777778 = -1.099943882 Simplifying s + 0.777777778 = -1.099943882 Reorder the terms: 0.777777778 + s = -1.099943882 Solving 0.777777778 + s = -1.099943882 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + s = -1.099943882 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + s = -1.099943882 + -0.777777778 s = -1.099943882 + -0.777777778 Combine like terms: -1.099943882 + -0.777777778 = -1.87772166 s = -1.87772166 Simplifying s = -1.87772166Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.322166104, -1.87772166}
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