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Simplifying 4s2 = 8s + 9 Reorder the terms: 4s2 = 9 + 8s Solving 4s2 = 9 + 8s Solving for variable 's'. Reorder the terms: -9 + -8s + 4s2 = 9 + 8s + -9 + -8s Reorder the terms: -9 + -8s + 4s2 = 9 + -9 + 8s + -8s Combine like terms: 9 + -9 = 0 -9 + -8s + 4s2 = 0 + 8s + -8s -9 + -8s + 4s2 = 8s + -8s Combine like terms: 8s + -8s = 0 -9 + -8s + 4s2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -2s + s2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -2s + 2.25 + s2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -2s + s2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -2s + s2 = 0 + 2.25 -2s + s2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -2s + s2 = 2.25 The s term is -2s. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2s + 1 + s2 = 2.25 + 1 Reorder the terms: 1 + -2s + s2 = 2.25 + 1 Combine like terms: 2.25 + 1 = 3.25 1 + -2s + s2 = 3.25 Factor a perfect square on the left side: (s + -1)(s + -1) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (s + -1) equal to 1.802775638 and -1.802775638.Subproblem 1
s + -1 = 1.802775638 Simplifying s + -1 = 1.802775638 Reorder the terms: -1 + s = 1.802775638 Solving -1 + s = 1.802775638 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = 1.802775638 + 1 Combine like terms: -1 + 1 = 0 0 + s = 1.802775638 + 1 s = 1.802775638 + 1 Combine like terms: 1.802775638 + 1 = 2.802775638 s = 2.802775638 Simplifying s = 2.802775638Subproblem 2
s + -1 = -1.802775638 Simplifying s + -1 = -1.802775638 Reorder the terms: -1 + s = -1.802775638 Solving -1 + s = -1.802775638 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + s = -1.802775638 + 1 Combine like terms: -1 + 1 = 0 0 + s = -1.802775638 + 1 s = -1.802775638 + 1 Combine like terms: -1.802775638 + 1 = -0.802775638 s = -0.802775638 Simplifying s = -0.802775638Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.802775638, -0.802775638}
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