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Simplifying s2 + -12s + 30 = 0 Reorder the terms: 30 + -12s + s2 = 0 Solving 30 + -12s + s2 = 0 Solving for variable 's'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12s + -30 + s2 = 0 + -30 Reorder the terms: 30 + -30 + -12s + s2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12s + s2 = 0 + -30 -12s + s2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12s + s2 = -30 The s term is -12s. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12s + 36 + s2 = -30 + 36 Reorder the terms: 36 + -12s + s2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12s + s2 = 6 Factor a perfect square on the left side: (s + -6)(s + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (s + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
s + -6 = 2.449489743 Simplifying s + -6 = 2.449489743 Reorder the terms: -6 + s = 2.449489743 Solving -6 + s = 2.449489743 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + s = 2.449489743 + 6 s = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 s = 8.449489743 Simplifying s = 8.449489743Subproblem 2
s + -6 = -2.449489743 Simplifying s + -6 = -2.449489743 Reorder the terms: -6 + s = -2.449489743 Solving -6 + s = -2.449489743 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + s = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + s = -2.449489743 + 6 s = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 s = 3.550510257 Simplifying s = 3.550510257Solution
The solution to the problem is based on the solutions from the subproblems. s = {8.449489743, 3.550510257}
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