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Simplifying m(m + -3) + 3m = 7m + 43 Reorder the terms: m(-3 + m) + 3m = 7m + 43 (-3 * m + m * m) + 3m = 7m + 43 (-3m + m2) + 3m = 7m + 43 Reorder the terms: -3m + 3m + m2 = 7m + 43 Combine like terms: -3m + 3m = 0 0 + m2 = 7m + 43 m2 = 7m + 43 Reorder the terms: m2 = 43 + 7m Solving m2 = 43 + 7m Solving for variable 'm'. Reorder the terms: -43 + -7m + m2 = 43 + 7m + -43 + -7m Reorder the terms: -43 + -7m + m2 = 43 + -43 + 7m + -7m Combine like terms: 43 + -43 = 0 -43 + -7m + m2 = 0 + 7m + -7m -43 + -7m + m2 = 7m + -7m Combine like terms: 7m + -7m = 0 -43 + -7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -7m + 43 + m2 = 0 + 43 Reorder the terms: -43 + 43 + -7m + m2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -7m + m2 = 0 + 43 -7m + m2 = 0 + 43 Combine like terms: 0 + 43 = 43 -7m + m2 = 43 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 = 43 + 12.25 Reorder the terms: 12.25 + -7m + m2 = 43 + 12.25 Combine like terms: 43 + 12.25 = 55.25 12.25 + -7m + m2 = 55.25 Factor a perfect square on the left side: (m + -3.5)(m + -3.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (m + -3.5) equal to 7.433034374 and -7.433034374.Subproblem 1
m + -3.5 = 7.433034374 Simplifying m + -3.5 = 7.433034374 Reorder the terms: -3.5 + m = 7.433034374 Solving -3.5 + m = 7.433034374 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 = 7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = 7.433034374 + 3.5 m = 7.433034374 + 3.5 Combine like terms: 7.433034374 + 3.5 = 10.933034374 m = 10.933034374 Simplifying m = 10.933034374Subproblem 2
m + -3.5 = -7.433034374 Simplifying m + -3.5 = -7.433034374 Reorder the terms: -3.5 + m = -7.433034374 Solving -3.5 + m = -7.433034374 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 = -7.433034374 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = -7.433034374 + 3.5 m = -7.433034374 + 3.5 Combine like terms: -7.433034374 + 3.5 = -3.933034374 m = -3.933034374 Simplifying m = -3.933034374Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.933034374, -3.933034374}
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