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Simplifying -10m + -3 = m2 Reorder the terms: -3 + -10m = m2 Solving -3 + -10m = m2 Solving for variable 'm'. Combine like terms: m2 + -1m2 = 0 -3 + -10m + -1m2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 10m + m2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 10m + m2)' equal to zero and attempt to solve: Simplifying 3 + 10m + m2 = 0 Solving 3 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 10m + -3 + m2 = 0 + -3 Reorder the terms: 3 + -3 + 10m + m2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10m + m2 = 0 + -3 10m + m2 = 0 + -3 Combine like terms: 0 + -3 = -3 10m + m2 = -3 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = -3 + 25 Reorder the terms: 25 + 10m + m2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + 10m + m2 = 22 Factor a perfect square on the left side: (m + 5)(m + 5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (m + 5) equal to 4.69041576 and -4.69041576.Subproblem 1
m + 5 = 4.69041576 Simplifying m + 5 = 4.69041576 Reorder the terms: 5 + m = 4.69041576 Solving 5 + m = 4.69041576 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + m = 4.69041576 + -5 m = 4.69041576 + -5 Combine like terms: 4.69041576 + -5 = -0.30958424 m = -0.30958424 Simplifying m = -0.30958424Subproblem 2
m + 5 = -4.69041576 Simplifying m + 5 = -4.69041576 Reorder the terms: 5 + m = -4.69041576 Solving 5 + m = -4.69041576 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -4.69041576 + -5 Combine like terms: 5 + -5 = 0 0 + m = -4.69041576 + -5 m = -4.69041576 + -5 Combine like terms: -4.69041576 + -5 = -9.69041576 m = -9.69041576 Simplifying m = -9.69041576Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.30958424, -9.69041576}Solution
m = {-0.30958424, -9.69041576}
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