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Simplifying (7s2 + 6s + -3) + -1(-6s + -1) = 0 Reorder the terms: (-3 + 6s + 7s2) + -1(-6s + -1) = 0 Remove parenthesis around (-3 + 6s + 7s2) -3 + 6s + 7s2 + -1(-6s + -1) = 0 Reorder the terms: -3 + 6s + 7s2 + -1(-1 + -6s) = 0 -3 + 6s + 7s2 + (-1 * -1 + -6s * -1) = 0 -3 + 6s + 7s2 + (1 + 6s) = 0 Reorder the terms: -3 + 1 + 6s + 6s + 7s2 = 0 Combine like terms: -3 + 1 = -2 -2 + 6s + 6s + 7s2 = 0 Combine like terms: 6s + 6s = 12s -2 + 12s + 7s2 = 0 Solving -2 + 12s + 7s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 1.714285714s + s2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.714285714s + 0.2857142857 + s2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.714285714s + s2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.714285714s + s2 = 0 + 0.2857142857 1.714285714s + s2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.714285714s + s2 = 0.2857142857 The s term is 1.714285714s. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714s + 0.7346938773 + s2 = 0.2857142857 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714s + s2 = 0.2857142857 + 0.7346938773 Combine like terms: 0.2857142857 + 0.7346938773 = 1.020408163 0.7346938773 + 1.714285714s + s2 = 1.020408163 Factor a perfect square on the left side: (s + 0.857142857)(s + 0.857142857) = 1.020408163 Calculate the square root of the right side: 1.010152544 Break this problem into two subproblems by setting (s + 0.857142857) equal to 1.010152544 and -1.010152544.Subproblem 1
s + 0.857142857 = 1.010152544 Simplifying s + 0.857142857 = 1.010152544 Reorder the terms: 0.857142857 + s = 1.010152544 Solving 0.857142857 + s = 1.010152544 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + s = 1.010152544 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + s = 1.010152544 + -0.857142857 s = 1.010152544 + -0.857142857 Combine like terms: 1.010152544 + -0.857142857 = 0.153009687 s = 0.153009687 Simplifying s = 0.153009687Subproblem 2
s + 0.857142857 = -1.010152544 Simplifying s + 0.857142857 = -1.010152544 Reorder the terms: 0.857142857 + s = -1.010152544 Solving 0.857142857 + s = -1.010152544 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + s = -1.010152544 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + s = -1.010152544 + -0.857142857 s = -1.010152544 + -0.857142857 Combine like terms: -1.010152544 + -0.857142857 = -1.867295401 s = -1.867295401 Simplifying s = -1.867295401Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.153009687, -1.867295401}
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