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Simplifying 10s2 + -7s + -9 = 0 Reorder the terms: -9 + -7s + 10s2 = 0 Solving -9 + -7s + 10s2 = 0 Solving for variable 's'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + -0.7s + s2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -0.7s + 0.9 + s2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -0.7s + s2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -0.7s + s2 = 0 + 0.9 -0.7s + s2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -0.7s + s2 = 0.9 The s term is -0.7s. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7s + 0.1225 + s2 = 0.9 + 0.1225 Reorder the terms: 0.1225 + -0.7s + s2 = 0.9 + 0.1225 Combine like terms: 0.9 + 0.1225 = 1.0225 0.1225 + -0.7s + s2 = 1.0225 Factor a perfect square on the left side: (s + -0.35)(s + -0.35) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (s + -0.35) equal to 1.011187421 and -1.011187421.Subproblem 1
s + -0.35 = 1.011187421 Simplifying s + -0.35 = 1.011187421 Reorder the terms: -0.35 + s = 1.011187421 Solving -0.35 + s = 1.011187421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + s = 1.011187421 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + s = 1.011187421 + 0.35 s = 1.011187421 + 0.35 Combine like terms: 1.011187421 + 0.35 = 1.361187421 s = 1.361187421 Simplifying s = 1.361187421Subproblem 2
s + -0.35 = -1.011187421 Simplifying s + -0.35 = -1.011187421 Reorder the terms: -0.35 + s = -1.011187421 Solving -0.35 + s = -1.011187421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + s = -1.011187421 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + s = -1.011187421 + 0.35 s = -1.011187421 + 0.35 Combine like terms: -1.011187421 + 0.35 = -0.661187421 s = -0.661187421 Simplifying s = -0.661187421Solution
The solution to the problem is based on the solutions from the subproblems. s = {1.361187421, -0.661187421}
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