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Simplifying 4m(3m + 12) = m + 12 Reorder the terms: 4m(12 + 3m) = m + 12 (12 * 4m + 3m * 4m) = m + 12 (48m + 12m2) = m + 12 Reorder the terms: 48m + 12m2 = 12 + m Solving 48m + 12m2 = 12 + m Solving for variable 'm'. Reorder the terms: -12 + 48m + -1m + 12m2 = 12 + m + -12 + -1m Combine like terms: 48m + -1m = 47m -12 + 47m + 12m2 = 12 + m + -12 + -1m Reorder the terms: -12 + 47m + 12m2 = 12 + -12 + m + -1m Combine like terms: 12 + -12 = 0 -12 + 47m + 12m2 = 0 + m + -1m -12 + 47m + 12m2 = m + -1m Combine like terms: m + -1m = 0 -12 + 47m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + 3.916666667m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.916666667m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 3.916666667m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.916666667m + m2 = 0 + 1 3.916666667m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.916666667m + m2 = 1 The m term is 3.916666667m. Take half its coefficient (1.958333334). Square it (3.835069447) and add it to both sides. Add '3.835069447' to each side of the equation. 3.916666667m + 3.835069447 + m2 = 1 + 3.835069447 Reorder the terms: 3.835069447 + 3.916666667m + m2 = 1 + 3.835069447 Combine like terms: 1 + 3.835069447 = 4.835069447 3.835069447 + 3.916666667m + m2 = 4.835069447 Factor a perfect square on the left side: (m + 1.958333334)(m + 1.958333334) = 4.835069447 Calculate the square root of the right side: 2.198879134 Break this problem into two subproblems by setting (m + 1.958333334) equal to 2.198879134 and -2.198879134.Subproblem 1
m + 1.958333334 = 2.198879134 Simplifying m + 1.958333334 = 2.198879134 Reorder the terms: 1.958333334 + m = 2.198879134 Solving 1.958333334 + m = 2.198879134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + m = 2.198879134 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + m = 2.198879134 + -1.958333334 m = 2.198879134 + -1.958333334 Combine like terms: 2.198879134 + -1.958333334 = 0.2405458 m = 0.2405458 Simplifying m = 0.2405458Subproblem 2
m + 1.958333334 = -2.198879134 Simplifying m + 1.958333334 = -2.198879134 Reorder the terms: 1.958333334 + m = -2.198879134 Solving 1.958333334 + m = -2.198879134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + m = -2.198879134 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + m = -2.198879134 + -1.958333334 m = -2.198879134 + -1.958333334 Combine like terms: -2.198879134 + -1.958333334 = -4.157212468 m = -4.157212468 Simplifying m = -4.157212468Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.2405458, -4.157212468}
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