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Simplifying m2 = 4m + 19 Reorder the terms: m2 = 19 + 4m Solving m2 = 19 + 4m Solving for variable 'm'. Reorder the terms: -19 + -4m + m2 = 19 + 4m + -19 + -4m Reorder the terms: -19 + -4m + m2 = 19 + -19 + 4m + -4m Combine like terms: 19 + -19 = 0 -19 + -4m + m2 = 0 + 4m + -4m -19 + -4m + m2 = 4m + -4m Combine like terms: 4m + -4m = 0 -19 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -4m + 19 + m2 = 0 + 19 Reorder the terms: -19 + 19 + -4m + m2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4m + m2 = 0 + 19 -4m + m2 = 0 + 19 Combine like terms: 0 + 19 = 19 -4m + m2 = 19 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 19 + 4 Reorder the terms: 4 + -4m + m2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + -4m + m2 = 23 Factor a perfect square on the left side: (m + -2)(m + -2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (m + -2) equal to 4.795831523 and -4.795831523.Subproblem 1
m + -2 = 4.795831523 Simplifying m + -2 = 4.795831523 Reorder the terms: -2 + m = 4.795831523 Solving -2 + m = 4.795831523 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + m = 4.795831523 + 2 m = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 m = 6.795831523 Simplifying m = 6.795831523Subproblem 2
m + -2 = -4.795831523 Simplifying m + -2 = -4.795831523 Reorder the terms: -2 + m = -4.795831523 Solving -2 + m = -4.795831523 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + m = -4.795831523 + 2 m = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 m = -2.795831523 Simplifying m = -2.795831523Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.795831523, -2.795831523}
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