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Simplifying 6s2 + -13s + -10 = 0 Reorder the terms: -10 + -13s + 6s2 = 0 Solving -10 + -13s + 6s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.666666667 + -2.166666667s + s2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2.166666667s + 1.666666667 + s2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2.166666667s + s2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2.166666667s + s2 = 0 + 1.666666667 -2.166666667s + s2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2.166666667s + s2 = 1.666666667 The s term is -2.166666667s. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667s + 1.173611113 + s2 = 1.666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667s + s2 = 1.666666667 + 1.173611113 Combine like terms: 1.666666667 + 1.173611113 = 2.84027778 1.173611113 + -2.166666667s + s2 = 2.84027778 Factor a perfect square on the left side: (s + -1.083333334)(s + -1.083333334) = 2.84027778 Calculate the square root of the right side: 1.685312369 Break this problem into two subproblems by setting (s + -1.083333334) equal to 1.685312369 and -1.685312369.Subproblem 1
s + -1.083333334 = 1.685312369 Simplifying s + -1.083333334 = 1.685312369 Reorder the terms: -1.083333334 + s = 1.685312369 Solving -1.083333334 + s = 1.685312369 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + s = 1.685312369 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + s = 1.685312369 + 1.083333334 s = 1.685312369 + 1.083333334 Combine like terms: 1.685312369 + 1.083333334 = 2.768645703 s = 2.768645703 Simplifying s = 2.768645703Subproblem 2
s + -1.083333334 = -1.685312369 Simplifying s + -1.083333334 = -1.685312369 Reorder the terms: -1.083333334 + s = -1.685312369 Solving -1.083333334 + s = -1.685312369 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + s = -1.685312369 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + s = -1.685312369 + 1.083333334 s = -1.685312369 + 1.083333334 Combine like terms: -1.685312369 + 1.083333334 = -0.601979035 s = -0.601979035 Simplifying s = -0.601979035Solution
The solution to the problem is based on the solutions from the subproblems. s = {2.768645703, -0.601979035}
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