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Simplifying (s + 9)(s + -7) = 4 Reorder the terms: (9 + s)(s + -7) = 4 Reorder the terms: (9 + s)(-7 + s) = 4 Multiply (9 + s) * (-7 + s) (9(-7 + s) + s(-7 + s)) = 4 ((-7 * 9 + s * 9) + s(-7 + s)) = 4 ((-63 + 9s) + s(-7 + s)) = 4 (-63 + 9s + (-7 * s + s * s)) = 4 (-63 + 9s + (-7s + s2)) = 4 Combine like terms: 9s + -7s = 2s (-63 + 2s + s2) = 4 Solving -63 + 2s + s2 = 4 Solving for variable 's'. Reorder the terms: -63 + -4 + 2s + s2 = 4 + -4 Combine like terms: -63 + -4 = -67 -67 + 2s + s2 = 4 + -4 Combine like terms: 4 + -4 = 0 -67 + 2s + s2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 2s + 67 + s2 = 0 + 67 Reorder the terms: -67 + 67 + 2s + s2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 2s + s2 = 0 + 67 2s + s2 = 0 + 67 Combine like terms: 0 + 67 = 67 2s + s2 = 67 The s term is 2s. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2s + 1 + s2 = 67 + 1 Reorder the terms: 1 + 2s + s2 = 67 + 1 Combine like terms: 67 + 1 = 68 1 + 2s + s2 = 68 Factor a perfect square on the left side: (s + 1)(s + 1) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (s + 1) equal to 8.246211251 and -8.246211251.Subproblem 1
s + 1 = 8.246211251 Simplifying s + 1 = 8.246211251 Reorder the terms: 1 + s = 8.246211251 Solving 1 + s = 8.246211251 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = 8.246211251 + -1 Combine like terms: 1 + -1 = 0 0 + s = 8.246211251 + -1 s = 8.246211251 + -1 Combine like terms: 8.246211251 + -1 = 7.246211251 s = 7.246211251 Simplifying s = 7.246211251Subproblem 2
s + 1 = -8.246211251 Simplifying s + 1 = -8.246211251 Reorder the terms: 1 + s = -8.246211251 Solving 1 + s = -8.246211251 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + s = -8.246211251 + -1 Combine like terms: 1 + -1 = 0 0 + s = -8.246211251 + -1 s = -8.246211251 + -1 Combine like terms: -8.246211251 + -1 = -9.246211251 s = -9.246211251 Simplifying s = -9.246211251Solution
The solution to the problem is based on the solutions from the subproblems. s = {7.246211251, -9.246211251}
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