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Simplifying 4m2 + 2m = 18 Reorder the terms: 2m + 4m2 = 18 Solving 2m + 4m2 = 18 Solving for variable 'm'. Reorder the terms: -18 + 2m + 4m2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 2m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + m + 2m2)' equal to zero and attempt to solve: Simplifying -9 + m + 2m2 = 0 Solving -9 + m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 0.5m + m2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.5m + 4.5 + m2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.5m + m2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.5m + m2 = 0 + 4.5 0.5m + m2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.5m + m2 = 4.5 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5m + 0.25 + m2 = 4.5 + 0.25 Reorder the terms: 0.25 + 0.5m + m2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + 0.5m + m2 = 4.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (m + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
m + 0.5 = 2.179449472 Simplifying m + 0.5 = 2.179449472 Reorder the terms: 0.5 + m = 2.179449472 Solving 0.5 + m = 2.179449472 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 2.179449472 + -0.5 m = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 m = 1.679449472 Simplifying m = 1.679449472Subproblem 2
m + 0.5 = -2.179449472 Simplifying m + 0.5 = -2.179449472 Reorder the terms: 0.5 + m = -2.179449472 Solving 0.5 + m = -2.179449472 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -2.179449472 + -0.5 m = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 m = -2.679449472 Simplifying m = -2.679449472Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.679449472, -2.679449472}Solution
m = {1.679449472, -2.679449472}
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