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Simplifying 3s + 5s(s + -150) = 4730 Reorder the terms: 3s + 5s(-150 + s) = 4730 3s + (-150 * 5s + s * 5s) = 4730 3s + (-750s + 5s2) = 4730 Combine like terms: 3s + -750s = -747s -747s + 5s2 = 4730 Solving -747s + 5s2 = 4730 Solving for variable 's'. Reorder the terms: -4730 + -747s + 5s2 = 4730 + -4730 Combine like terms: 4730 + -4730 = 0 -4730 + -747s + 5s2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -946 + -149.4s + s2 = 0 Move the constant term to the right: Add '946' to each side of the equation. -946 + -149.4s + 946 + s2 = 0 + 946 Reorder the terms: -946 + 946 + -149.4s + s2 = 0 + 946 Combine like terms: -946 + 946 = 0 0 + -149.4s + s2 = 0 + 946 -149.4s + s2 = 0 + 946 Combine like terms: 0 + 946 = 946 -149.4s + s2 = 946 The s term is -149.4s. Take half its coefficient (-74.7). Square it (5580.09) and add it to both sides. Add '5580.09' to each side of the equation. -149.4s + 5580.09 + s2 = 946 + 5580.09 Reorder the terms: 5580.09 + -149.4s + s2 = 946 + 5580.09 Combine like terms: 946 + 5580.09 = 6526.09 5580.09 + -149.4s + s2 = 6526.09 Factor a perfect square on the left side: (s + -74.7)(s + -74.7) = 6526.09 Calculate the square root of the right side: 80.784218756 Break this problem into two subproblems by setting (s + -74.7) equal to 80.784218756 and -80.784218756.Subproblem 1
s + -74.7 = 80.784218756 Simplifying s + -74.7 = 80.784218756 Reorder the terms: -74.7 + s = 80.784218756 Solving -74.7 + s = 80.784218756 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '74.7' to each side of the equation. -74.7 + 74.7 + s = 80.784218756 + 74.7 Combine like terms: -74.7 + 74.7 = 0.0 0.0 + s = 80.784218756 + 74.7 s = 80.784218756 + 74.7 Combine like terms: 80.784218756 + 74.7 = 155.484218756 s = 155.484218756 Simplifying s = 155.484218756Subproblem 2
s + -74.7 = -80.784218756 Simplifying s + -74.7 = -80.784218756 Reorder the terms: -74.7 + s = -80.784218756 Solving -74.7 + s = -80.784218756 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '74.7' to each side of the equation. -74.7 + 74.7 + s = -80.784218756 + 74.7 Combine like terms: -74.7 + 74.7 = 0.0 0.0 + s = -80.784218756 + 74.7 s = -80.784218756 + 74.7 Combine like terms: -80.784218756 + 74.7 = -6.084218756 s = -6.084218756 Simplifying s = -6.084218756Solution
The solution to the problem is based on the solutions from the subproblems. s = {155.484218756, -6.084218756}
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