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Simplifying 3m + -2m(m + 7) = m + 4 Reorder the terms: 3m + -2m(7 + m) = m + 4 3m + (7 * -2m + m * -2m) = m + 4 3m + (-14m + -2m2) = m + 4 Combine like terms: 3m + -14m = -11m -11m + -2m2 = m + 4 Reorder the terms: -11m + -2m2 = 4 + m Solving -11m + -2m2 = 4 + m Solving for variable 'm'. Reorder the terms: -4 + -11m + -1m + -2m2 = 4 + m + -4 + -1m Combine like terms: -11m + -1m = -12m -4 + -12m + -2m2 = 4 + m + -4 + -1m Reorder the terms: -4 + -12m + -2m2 = 4 + -4 + m + -1m Combine like terms: 4 + -4 = 0 -4 + -12m + -2m2 = 0 + m + -1m -4 + -12m + -2m2 = m + -1m Combine like terms: m + -1m = 0 -4 + -12m + -2m2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 6m + m2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 6m + m2)' equal to zero and attempt to solve: Simplifying 2 + 6m + m2 = 0 Solving 2 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + 6m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6m + m2 = 0 + -2 6m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 6m + m2 = -2 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = -2 + 9 Reorder the terms: 9 + 6m + m2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6m + m2 = 7 Factor a perfect square on the left side: (m + 3)(m + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
m + 3 = 2.645751311 Simplifying m + 3 = 2.645751311 Reorder the terms: 3 + m = 2.645751311 Solving 3 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + m = 2.645751311 + -3 m = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 m = -0.354248689 Simplifying m = -0.354248689Subproblem 2
m + 3 = -2.645751311 Simplifying m + 3 = -2.645751311 Reorder the terms: 3 + m = -2.645751311 Solving 3 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + m = -2.645751311 + -3 m = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 m = -5.645751311 Simplifying m = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.354248689, -5.645751311}Solution
m = {-0.354248689, -5.645751311}
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