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Simplifying (10s2 + 5) + -1(5s2 + 3s + -2) = 0 Reorder the terms: (5 + 10s2) + -1(5s2 + 3s + -2) = 0 Remove parenthesis around (5 + 10s2) 5 + 10s2 + -1(5s2 + 3s + -2) = 0 Reorder the terms: 5 + 10s2 + -1(-2 + 3s + 5s2) = 0 5 + 10s2 + (-2 * -1 + 3s * -1 + 5s2 * -1) = 0 5 + 10s2 + (2 + -3s + -5s2) = 0 Reorder the terms: 5 + 2 + -3s + 10s2 + -5s2 = 0 Combine like terms: 5 + 2 = 7 7 + -3s + 10s2 + -5s2 = 0 Combine like terms: 10s2 + -5s2 = 5s2 7 + -3s + 5s2 = 0 Solving 7 + -3s + 5s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -0.6s + s2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -0.6s + -1.4 + s2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -0.6s + s2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -0.6s + s2 = 0 + -1.4 -0.6s + s2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -0.6s + s2 = -1.4 The s term is -0.6s. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6s + 0.09 + s2 = -1.4 + 0.09 Reorder the terms: 0.09 + -0.6s + s2 = -1.4 + 0.09 Combine like terms: -1.4 + 0.09 = -1.31 0.09 + -0.6s + s2 = -1.31 Factor a perfect square on the left side: (s + -0.3)(s + -0.3) = -1.31 Can't calculate square root of the right side. The solution to this equation could not be determined.
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