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Simplifying 8m2 + 16m + -38 = 0 Reorder the terms: -38 + 16m + 8m2 = 0 Solving -38 + 16m + 8m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 8m + 4m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 8m + 4m2)' equal to zero and attempt to solve: Simplifying -19 + 8m + 4m2 = 0 Solving -19 + 8m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + 2m + m2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 2m + 4.75 + m2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 2m + m2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 2m + m2 = 0 + 4.75 2m + m2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 2m + m2 = 4.75 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 4.75 + 1 Reorder the terms: 1 + 2m + m2 = 4.75 + 1 Combine like terms: 4.75 + 1 = 5.75 1 + 2m + m2 = 5.75 Factor a perfect square on the left side: (m + 1)(m + 1) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (m + 1) equal to 2.397915762 and -2.397915762.Subproblem 1
m + 1 = 2.397915762 Simplifying m + 1 = 2.397915762 Reorder the terms: 1 + m = 2.397915762 Solving 1 + m = 2.397915762 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 2.397915762 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.397915762 + -1 m = 2.397915762 + -1 Combine like terms: 2.397915762 + -1 = 1.397915762 m = 1.397915762 Simplifying m = 1.397915762Subproblem 2
m + 1 = -2.397915762 Simplifying m + 1 = -2.397915762 Reorder the terms: 1 + m = -2.397915762 Solving 1 + m = -2.397915762 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -2.397915762 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.397915762 + -1 m = -2.397915762 + -1 Combine like terms: -2.397915762 + -1 = -3.397915762 m = -3.397915762 Simplifying m = -3.397915762Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.397915762, -3.397915762}Solution
m = {1.397915762, -3.397915762}
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