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Simplifying 8m2 + 4m + -19 = 0 Reorder the terms: -19 + 4m + 8m2 = 0 Solving -19 + 4m + 8m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + 0.5m + m2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + 0.5m + 2.375 + m2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + 0.5m + m2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + 0.5m + m2 = 0 + 2.375 0.5m + m2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 0.5m + m2 = 2.375 The m term is 0.5m. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5m + 0.0625 + m2 = 2.375 + 0.0625 Reorder the terms: 0.0625 + 0.5m + m2 = 2.375 + 0.0625 Combine like terms: 2.375 + 0.0625 = 2.4375 0.0625 + 0.5m + m2 = 2.4375 Factor a perfect square on the left side: (m + 0.25)(m + 0.25) = 2.4375 Calculate the square root of the right side: 1.5612495 Break this problem into two subproblems by setting (m + 0.25) equal to 1.5612495 and -1.5612495.Subproblem 1
m + 0.25 = 1.5612495 Simplifying m + 0.25 = 1.5612495 Reorder the terms: 0.25 + m = 1.5612495 Solving 0.25 + m = 1.5612495 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = 1.5612495 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = 1.5612495 + -0.25 m = 1.5612495 + -0.25 Combine like terms: 1.5612495 + -0.25 = 1.3112495 m = 1.3112495 Simplifying m = 1.3112495Subproblem 2
m + 0.25 = -1.5612495 Simplifying m + 0.25 = -1.5612495 Reorder the terms: 0.25 + m = -1.5612495 Solving 0.25 + m = -1.5612495 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + m = -1.5612495 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + m = -1.5612495 + -0.25 m = -1.5612495 + -0.25 Combine like terms: -1.5612495 + -0.25 = -1.8112495 m = -1.8112495 Simplifying m = -1.8112495Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.3112495, -1.8112495}
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