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Simplifying 2s2 + -286s + -1717 = 0 Reorder the terms: -1717 + -286s + 2s2 = 0 Solving -1717 + -286s + 2s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -858.5 + -143s + s2 = 0 Move the constant term to the right: Add '858.5' to each side of the equation. -858.5 + -143s + 858.5 + s2 = 0 + 858.5 Reorder the terms: -858.5 + 858.5 + -143s + s2 = 0 + 858.5 Combine like terms: -858.5 + 858.5 = 0.0 0.0 + -143s + s2 = 0 + 858.5 -143s + s2 = 0 + 858.5 Combine like terms: 0 + 858.5 = 858.5 -143s + s2 = 858.5 The s term is -143s. Take half its coefficient (-71.5). Square it (5112.25) and add it to both sides. Add '5112.25' to each side of the equation. -143s + 5112.25 + s2 = 858.5 + 5112.25 Reorder the terms: 5112.25 + -143s + s2 = 858.5 + 5112.25 Combine like terms: 858.5 + 5112.25 = 5970.75 5112.25 + -143s + s2 = 5970.75 Factor a perfect square on the left side: (s + -71.5)(s + -71.5) = 5970.75 Calculate the square root of the right side: 77.270628314 Break this problem into two subproblems by setting (s + -71.5) equal to 77.270628314 and -77.270628314.Subproblem 1
s + -71.5 = 77.270628314 Simplifying s + -71.5 = 77.270628314 Reorder the terms: -71.5 + s = 77.270628314 Solving -71.5 + s = 77.270628314 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '71.5' to each side of the equation. -71.5 + 71.5 + s = 77.270628314 + 71.5 Combine like terms: -71.5 + 71.5 = 0.0 0.0 + s = 77.270628314 + 71.5 s = 77.270628314 + 71.5 Combine like terms: 77.270628314 + 71.5 = 148.770628314 s = 148.770628314 Simplifying s = 148.770628314Subproblem 2
s + -71.5 = -77.270628314 Simplifying s + -71.5 = -77.270628314 Reorder the terms: -71.5 + s = -77.270628314 Solving -71.5 + s = -77.270628314 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '71.5' to each side of the equation. -71.5 + 71.5 + s = -77.270628314 + 71.5 Combine like terms: -71.5 + 71.5 = 0.0 0.0 + s = -77.270628314 + 71.5 s = -77.270628314 + 71.5 Combine like terms: -77.270628314 + 71.5 = -5.770628314 s = -5.770628314 Simplifying s = -5.770628314Solution
The solution to the problem is based on the solutions from the subproblems. s = {148.770628314, -5.770628314}
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