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Simplifying s2 + -14s = -19 Reorder the terms: -14s + s2 = -19 Solving -14s + s2 = -19 Solving for variable 's'. Reorder the terms: 19 + -14s + s2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -14s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14s + -19 + s2 = 0 + -19 Reorder the terms: 19 + -19 + -14s + s2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14s + s2 = 0 + -19 -14s + s2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14s + s2 = -19 The s term is -14s. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14s + 49 + s2 = -19 + 49 Reorder the terms: 49 + -14s + s2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + -14s + s2 = 30 Factor a perfect square on the left side: (s + -7)(s + -7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (s + -7) equal to 5.477225575 and -5.477225575.Subproblem 1
s + -7 = 5.477225575 Simplifying s + -7 = 5.477225575 Reorder the terms: -7 + s = 5.477225575 Solving -7 + s = 5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = 5.477225575 + 7 s = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 s = 12.477225575 Simplifying s = 12.477225575Subproblem 2
s + -7 = -5.477225575 Simplifying s + -7 = -5.477225575 Reorder the terms: -7 + s = -5.477225575 Solving -7 + s = -5.477225575 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + s = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + s = -5.477225575 + 7 s = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 s = 1.522774425 Simplifying s = 1.522774425Solution
The solution to the problem is based on the solutions from the subproblems. s = {12.477225575, 1.522774425}
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