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Simplifying (-3s2 + 3s + 7) + -1(7s2 + 6s + -3) = 0 Reorder the terms: (7 + 3s + -3s2) + -1(7s2 + 6s + -3) = 0 Remove parenthesis around (7 + 3s + -3s2) 7 + 3s + -3s2 + -1(7s2 + 6s + -3) = 0 Reorder the terms: 7 + 3s + -3s2 + -1(-3 + 6s + 7s2) = 0 7 + 3s + -3s2 + (-3 * -1 + 6s * -1 + 7s2 * -1) = 0 7 + 3s + -3s2 + (3 + -6s + -7s2) = 0 Reorder the terms: 7 + 3 + 3s + -6s + -3s2 + -7s2 = 0 Combine like terms: 7 + 3 = 10 10 + 3s + -6s + -3s2 + -7s2 = 0 Combine like terms: 3s + -6s = -3s 10 + -3s + -3s2 + -7s2 = 0 Combine like terms: -3s2 + -7s2 = -10s2 10 + -3s + -10s2 = 0 Solving 10 + -3s + -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'. -1 + 0.3s + s2 = 0.0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.3s + 1 + s2 = 0.0 + 1 Reorder the terms: -1 + 1 + 0.3s + s2 = 0.0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.3s + s2 = 0.0 + 1 0.3s + s2 = 0.0 + 1 Combine like terms: 0.0 + 1 = 1 0.3s + s2 = 1 The s term is 0.3s. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3s + 0.0225 + s2 = 1 + 0.0225 Reorder the terms: 0.0225 + 0.3s + s2 = 1 + 0.0225 Combine like terms: 1 + 0.0225 = 1.0225 0.0225 + 0.3s + s2 = 1.0225 Factor a perfect square on the left side: (s + 0.15)(s + 0.15) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (s + 0.15) equal to 1.011187421 and -1.011187421.Subproblem 1
s + 0.15 = 1.011187421 Simplifying s + 0.15 = 1.011187421 Reorder the terms: 0.15 + s = 1.011187421 Solving 0.15 + s = 1.011187421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + s = 1.011187421 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + s = 1.011187421 + -0.15 s = 1.011187421 + -0.15 Combine like terms: 1.011187421 + -0.15 = 0.861187421 s = 0.861187421 Simplifying s = 0.861187421Subproblem 2
s + 0.15 = -1.011187421 Simplifying s + 0.15 = -1.011187421 Reorder the terms: 0.15 + s = -1.011187421 Solving 0.15 + s = -1.011187421 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + s = -1.011187421 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + s = -1.011187421 + -0.15 s = -1.011187421 + -0.15 Combine like terms: -1.011187421 + -0.15 = -1.161187421 s = -1.161187421 Simplifying s = -1.161187421Solution
The solution to the problem is based on the solutions from the subproblems. s = {0.861187421, -1.161187421}
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