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Simplifying (m2 + 7m + 89) = 77 * 18 Reorder the terms: (89 + 7m + m2) = 77 * 18 Remove parenthesis around (89 + 7m + m2) 89 + 7m + m2 = 77 * 18 Multiply 77 * 18 89 + 7m + m2 = 1386 Solving 89 + 7m + m2 = 1386 Solving for variable 'm'. Reorder the terms: 89 + -1386 + 7m + m2 = 1386 + -1386 Combine like terms: 89 + -1386 = -1297 -1297 + 7m + m2 = 1386 + -1386 Combine like terms: 1386 + -1386 = 0 -1297 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '1297' to each side of the equation. -1297 + 7m + 1297 + m2 = 0 + 1297 Reorder the terms: -1297 + 1297 + 7m + m2 = 0 + 1297 Combine like terms: -1297 + 1297 = 0 0 + 7m + m2 = 0 + 1297 7m + m2 = 0 + 1297 Combine like terms: 0 + 1297 = 1297 7m + m2 = 1297 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 1297 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 1297 + 12.25 Combine like terms: 1297 + 12.25 = 1309.25 12.25 + 7m + m2 = 1309.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 1309.25 Calculate the square root of the right side: 36.183559803 Break this problem into two subproblems by setting (m + 3.5) equal to 36.183559803 and -36.183559803.Subproblem 1
m + 3.5 = 36.183559803 Simplifying m + 3.5 = 36.183559803 Reorder the terms: 3.5 + m = 36.183559803 Solving 3.5 + m = 36.183559803 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 36.183559803 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 36.183559803 + -3.5 m = 36.183559803 + -3.5 Combine like terms: 36.183559803 + -3.5 = 32.683559803 m = 32.683559803 Simplifying m = 32.683559803Subproblem 2
m + 3.5 = -36.183559803 Simplifying m + 3.5 = -36.183559803 Reorder the terms: 3.5 + m = -36.183559803 Solving 3.5 + m = -36.183559803 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -36.183559803 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -36.183559803 + -3.5 m = -36.183559803 + -3.5 Combine like terms: -36.183559803 + -3.5 = -39.683559803 m = -39.683559803 Simplifying m = -39.683559803Solution
The solution to the problem is based on the solutions from the subproblems. m = {32.683559803, -39.683559803}
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