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Simplifying (5s2) + -1(2s + -1s) = 47.921015 Combine like terms: 2s + -1s = 1s (5s2) + -1(1s) = 47.921015 Remove parenthesis around (1s) (5s2) + -1 * 1s = 47.921015 Multiply -1 * 1 (5s2) + -1s = 47.921015 Reorder the terms: -1s + (5s2) = 47.921015 Solving -1s + (5s2) = 47.921015 Solving for variable 's'. Reorder the terms: -47.921015 + -1s + (5s2) = 47.921015 + -47.921015 Combine like terms: 47.921015 + -47.921015 = 0.000000 -47.921015 + -1s + (5s2) = 0.000000 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.584203 + -0.2s + s2 = 0.000000 Move the constant term to the right: Add '9.584203' to each side of the equation. -9.584203 + -0.2s + 9.584203 + s2 = 0.000000 + 9.584203 Reorder the terms: -9.584203 + 9.584203 + -0.2s + s2 = 0.000000 + 9.584203 Combine like terms: -9.584203 + 9.584203 = 0.000000 0.000000 + -0.2s + s2 = 0.000000 + 9.584203 -0.2s + s2 = 0.000000 + 9.584203 Combine like terms: 0.000000 + 9.584203 = 9.584203 -0.2s + s2 = 9.584203 The s term is -0.2s. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2s + 0.01 + s2 = 9.584203 + 0.01 Reorder the terms: 0.01 + -0.2s + s2 = 9.584203 + 0.01 Combine like terms: 9.584203 + 0.01 = 9.594203 0.01 + -0.2s + s2 = 9.594203 Factor a perfect square on the left side: ((s) + -0.1)((s) + -0.1) = 9.594203 Calculate the square root of the right side: 3.097451049 Break this problem into two subproblems by setting ((s) + -0.1) equal to 3.097451049 and -3.097451049.Subproblem 1
(s) + -0.1 = 3.097451049 Simplifying (s) + -0.1 = 3.097451049 s + -0.1 = 3.097451049 Reorder the terms: -0.1 + s = 3.097451049 Solving -0.1 + s = 3.097451049 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + s = 3.097451049 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + s = 3.097451049 + 0.1 s = 3.097451049 + 0.1 Combine like terms: 3.097451049 + 0.1 = 3.197451049 s = 3.197451049 Simplifying s = 3.197451049Subproblem 2
(s) + -0.1 = -3.097451049 Simplifying (s) + -0.1 = -3.097451049 s + -0.1 = -3.097451049 Reorder the terms: -0.1 + s = -3.097451049 Solving -0.1 + s = -3.097451049 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + s = -3.097451049 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + s = -3.097451049 + 0.1 s = -3.097451049 + 0.1 Combine like terms: -3.097451049 + 0.1 = -2.997451049 s = -2.997451049 Simplifying s = -2.997451049Solution
The solution to the problem is based on the solutions from the subproblems. s = {3.197451049, -2.997451049}
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