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Simplifying s2 + -29s + 6 = 0 Reorder the terms: 6 + -29s + s2 = 0 Solving 6 + -29s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -29s + -6 + s2 = 0 + -6 Reorder the terms: 6 + -6 + -29s + s2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -29s + s2 = 0 + -6 -29s + s2 = 0 + -6 Combine like terms: 0 + -6 = -6 -29s + s2 = -6 The s term is -29s. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29s + 210.25 + s2 = -6 + 210.25 Reorder the terms: 210.25 + -29s + s2 = -6 + 210.25 Combine like terms: -6 + 210.25 = 204.25 210.25 + -29s + s2 = 204.25 Factor a perfect square on the left side: (s + -14.5)(s + -14.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (s + -14.5) equal to 14.291605928 and -14.291605928.Subproblem 1
s + -14.5 = 14.291605928 Simplifying s + -14.5 = 14.291605928 Reorder the terms: -14.5 + s = 14.291605928 Solving -14.5 + s = 14.291605928 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + s = 14.291605928 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + s = 14.291605928 + 14.5 s = 14.291605928 + 14.5 Combine like terms: 14.291605928 + 14.5 = 28.791605928 s = 28.791605928 Simplifying s = 28.791605928Subproblem 2
s + -14.5 = -14.291605928 Simplifying s + -14.5 = -14.291605928 Reorder the terms: -14.5 + s = -14.291605928 Solving -14.5 + s = -14.291605928 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + s = -14.291605928 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + s = -14.291605928 + 14.5 s = -14.291605928 + 14.5 Combine like terms: -14.291605928 + 14.5 = 0.208394072 s = 0.208394072 Simplifying s = 0.208394072Solution
The solution to the problem is based on the solutions from the subproblems. s = {28.791605928, 0.208394072}
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