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Simplifying 5s2 + -35s + -32 = 0 Reorder the terms: -32 + -35s + 5s2 = 0 Solving -32 + -35s + 5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + -7s + s2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -7s + 6.4 + s2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -7s + s2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -7s + s2 = 0 + 6.4 -7s + s2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -7s + s2 = 6.4 The s term is -7s. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7s + 12.25 + s2 = 6.4 + 12.25 Reorder the terms: 12.25 + -7s + s2 = 6.4 + 12.25 Combine like terms: 6.4 + 12.25 = 18.65 12.25 + -7s + s2 = 18.65 Factor a perfect square on the left side: (s + -3.5)(s + -3.5) = 18.65 Calculate the square root of the right side: 4.318564576 Break this problem into two subproblems by setting (s + -3.5) equal to 4.318564576 and -4.318564576.Subproblem 1
s + -3.5 = 4.318564576 Simplifying s + -3.5 = 4.318564576 Reorder the terms: -3.5 + s = 4.318564576 Solving -3.5 + s = 4.318564576 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + s = 4.318564576 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + s = 4.318564576 + 3.5 s = 4.318564576 + 3.5 Combine like terms: 4.318564576 + 3.5 = 7.818564576 s = 7.818564576 Simplifying s = 7.818564576Subproblem 2
s + -3.5 = -4.318564576 Simplifying s + -3.5 = -4.318564576 Reorder the terms: -3.5 + s = -4.318564576 Solving -3.5 + s = -4.318564576 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + s = -4.318564576 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + s = -4.318564576 + 3.5 s = -4.318564576 + 3.5 Combine like terms: -4.318564576 + 3.5 = -0.818564576 s = -0.818564576 Simplifying s = -0.818564576Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.818564576, -0.818564576}
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