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Simplifying 2(s + 3) * 4s + -5 = 0 Reorder the terms: 2(3 + s) * 4s + -5 = 0 Reorder the terms for easier multiplication: 2 * 4s(3 + s) + -5 = 0 Multiply 2 * 4 8s(3 + s) + -5 = 0 (3 * 8s + s * 8s) + -5 = 0 (24s + 8s2) + -5 = 0 Reorder the terms: -5 + 24s + 8s2 = 0 Solving -5 + 24s + 8s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 3s + s2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 3s + 0.625 + s2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 3s + s2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 3s + s2 = 0 + 0.625 3s + s2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 3s + s2 = 0.625 The s term is 3s. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3s + 2.25 + s2 = 0.625 + 2.25 Reorder the terms: 2.25 + 3s + s2 = 0.625 + 2.25 Combine like terms: 0.625 + 2.25 = 2.875 2.25 + 3s + s2 = 2.875 Factor a perfect square on the left side: (s + 1.5)(s + 1.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (s + 1.5) equal to 1.695582496 and -1.695582496.Subproblem 1
s + 1.5 = 1.695582496 Simplifying s + 1.5 = 1.695582496 Reorder the terms: 1.5 + s = 1.695582496 Solving 1.5 + s = 1.695582496 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = 1.695582496 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = 1.695582496 + -1.5 s = 1.695582496 + -1.5 Combine like terms: 1.695582496 + -1.5 = 0.195582496 s = 0.195582496 Simplifying s = 0.195582496Subproblem 2
s + 1.5 = -1.695582496 Simplifying s + 1.5 = -1.695582496 Reorder the terms: 1.5 + s = -1.695582496 Solving 1.5 + s = -1.695582496 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = -1.695582496 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = -1.695582496 + -1.5 s = -1.695582496 + -1.5 Combine like terms: -1.695582496 + -1.5 = -3.195582496 s = -3.195582496 Simplifying s = -3.195582496Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.195582496, -3.195582496}
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