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Simplifying 7s2 + 5s + -50 = 0 Reorder the terms: -50 + 5s + 7s2 = 0 Solving -50 + 5s + 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'. -7.142857143 + 0.7142857143s + s2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 0.7142857143s + 7.142857143 + s2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 0.7142857143s + s2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 0.7142857143s + s2 = 0 + 7.142857143 0.7142857143s + s2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 0.7142857143s + s2 = 7.142857143 The s term is 0.7142857143s. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143s + 0.1275510204 + s2 = 7.142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143s + s2 = 7.142857143 + 0.1275510204 Combine like terms: 7.142857143 + 0.1275510204 = 7.2704081634 0.1275510204 + 0.7142857143s + s2 = 7.2704081634 Factor a perfect square on the left side: (s + 0.3571428572)(s + 0.3571428572) = 7.2704081634 Calculate the square root of the right side: 2.696369441 Break this problem into two subproblems by setting (s + 0.3571428572) equal to 2.696369441 and -2.696369441.Subproblem 1
s + 0.3571428572 = 2.696369441 Simplifying s + 0.3571428572 = 2.696369441 Reorder the terms: 0.3571428572 + s = 2.696369441 Solving 0.3571428572 + s = 2.696369441 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + s = 2.696369441 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + s = 2.696369441 + -0.3571428572 s = 2.696369441 + -0.3571428572 Combine like terms: 2.696369441 + -0.3571428572 = 2.3392265838 s = 2.3392265838 Simplifying s = 2.3392265838Subproblem 2
s + 0.3571428572 = -2.696369441 Simplifying s + 0.3571428572 = -2.696369441 Reorder the terms: 0.3571428572 + s = -2.696369441 Solving 0.3571428572 + s = -2.696369441 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + s = -2.696369441 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + s = -2.696369441 + -0.3571428572 s = -2.696369441 + -0.3571428572 Combine like terms: -2.696369441 + -0.3571428572 = -3.0535122982 s = -3.0535122982 Simplifying s = -3.0535122982Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.3392265838, -3.0535122982}
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