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Simplifying 49s2 + 42s = 9 Reorder the terms: 42s + 49s2 = 9 Solving 42s + 49s2 = 9 Solving for variable 's'. Reorder the terms: -9 + 42s + 49s2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 42s + 49s2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1836734694 + 0.8571428571s + s2 = 0 Move the constant term to the right: Add '0.1836734694' to each side of the equation. -0.1836734694 + 0.8571428571s + 0.1836734694 + s2 = 0 + 0.1836734694 Reorder the terms: -0.1836734694 + 0.1836734694 + 0.8571428571s + s2 = 0 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + 0.8571428571s + s2 = 0 + 0.1836734694 0.8571428571s + s2 = 0 + 0.1836734694 Combine like terms: 0 + 0.1836734694 = 0.1836734694 0.8571428571s + s2 = 0.1836734694 The s term is 0.8571428571s. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571s + 0.1836734694 + s2 = 0.1836734694 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571s + s2 = 0.1836734694 + 0.1836734694 Combine like terms: 0.1836734694 + 0.1836734694 = 0.3673469388 0.1836734694 + 0.8571428571s + s2 = 0.3673469388 Factor a perfect square on the left side: (s + 0.4285714286)(s + 0.4285714286) = 0.3673469388 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (s + 0.4285714286) equal to 0.606091527 and -0.606091527.Subproblem 1
s + 0.4285714286 = 0.606091527 Simplifying s + 0.4285714286 = 0.606091527 Reorder the terms: 0.4285714286 + s = 0.606091527 Solving 0.4285714286 + s = 0.606091527 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + s = 0.606091527 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + s = 0.606091527 + -0.4285714286 s = 0.606091527 + -0.4285714286 Combine like terms: 0.606091527 + -0.4285714286 = 0.1775200984 s = 0.1775200984 Simplifying s = 0.1775200984Subproblem 2
s + 0.4285714286 = -0.606091527 Simplifying s + 0.4285714286 = -0.606091527 Reorder the terms: 0.4285714286 + s = -0.606091527 Solving 0.4285714286 + s = -0.606091527 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + s = -0.606091527 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + s = -0.606091527 + -0.4285714286 s = -0.606091527 + -0.4285714286 Combine like terms: -0.606091527 + -0.4285714286 = -1.0346629556 s = -1.0346629556 Simplifying s = -1.0346629556Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.1775200984, -1.0346629556}
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