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Simplifying 35s2 + 10s + -50 = 0 Reorder the terms: -50 + 10s + 35s2 = 0 Solving -50 + 10s + 35s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + 2s + 7s2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-10 + 2s + 7s2)' equal to zero and attempt to solve: Simplifying -10 + 2s + 7s2 = 0 Solving -10 + 2s + 7s2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + 0.2857142857s + s2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.2857142857s + 1.428571429 + s2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.2857142857s + s2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.2857142857s + s2 = 0 + 1.428571429 0.2857142857s + s2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.2857142857s + s2 = 1.428571429 The s term is 0.2857142857s. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857s + 0.02040816328 + s2 = 1.428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857s + s2 = 1.428571429 + 0.02040816328 Combine like terms: 1.428571429 + 0.02040816328 = 1.44897959228 0.02040816328 + 0.2857142857s + s2 = 1.44897959228 Factor a perfect square on the left side: (s + 0.1428571429)(s + 0.1428571429) = 1.44897959228 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (s + 0.1428571429) equal to 1.203735682 and -1.203735682.Subproblem 1
s + 0.1428571429 = 1.203735682 Simplifying s + 0.1428571429 = 1.203735682 Reorder the terms: 0.1428571429 + s = 1.203735682 Solving 0.1428571429 + s = 1.203735682 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + s = 1.203735682 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + s = 1.203735682 + -0.1428571429 s = 1.203735682 + -0.1428571429 Combine like terms: 1.203735682 + -0.1428571429 = 1.0608785391 s = 1.0608785391 Simplifying s = 1.0608785391Subproblem 2
s + 0.1428571429 = -1.203735682 Simplifying s + 0.1428571429 = -1.203735682 Reorder the terms: 0.1428571429 + s = -1.203735682 Solving 0.1428571429 + s = -1.203735682 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + s = -1.203735682 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + s = -1.203735682 + -0.1428571429 s = -1.203735682 + -0.1428571429 Combine like terms: -1.203735682 + -0.1428571429 = -1.3465928249 s = -1.3465928249 Simplifying s = -1.3465928249Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.0608785391, -1.3465928249}Solution
s = {1.0608785391, -1.3465928249}
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