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Simplifying m2 + -3m = 7 Reorder the terms: -3m + m2 = 7 Solving -3m + m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + -3m + m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -3m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -3m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3m + m2 = 0 + 7 -3m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3m + m2 = 7 The m term is -3m. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3m + 2.25 + m2 = 7 + 2.25 Reorder the terms: 2.25 + -3m + m2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + -3m + m2 = 9.25 Factor a perfect square on the left side: (m + -1.5)(m + -1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (m + -1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
m + -1.5 = 3.041381265 Simplifying m + -1.5 = 3.041381265 Reorder the terms: -1.5 + m = 3.041381265 Solving -1.5 + m = 3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = 3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 3.041381265 + 1.5 m = 3.041381265 + 1.5 Combine like terms: 3.041381265 + 1.5 = 4.541381265 m = 4.541381265 Simplifying m = 4.541381265Subproblem 2
m + -1.5 = -3.041381265 Simplifying m + -1.5 = -3.041381265 Reorder the terms: -1.5 + m = -3.041381265 Solving -1.5 + m = -3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = -3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -3.041381265 + 1.5 m = -3.041381265 + 1.5 Combine like terms: -3.041381265 + 1.5 = -1.541381265 m = -1.541381265 Simplifying m = -1.541381265Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.541381265, -1.541381265}
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