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Simplifying 10m2 + 30m + 5 = 0 Reorder the terms: 5 + 30m + 10m2 = 0 Solving 5 + 30m + 10m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '5'. 5(1 + 6m + 2m2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + 6m + 2m2)' equal to zero and attempt to solve: Simplifying 1 + 6m + 2m2 = 0 Solving 1 + 6m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 3m + m2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 3m + -0.5 + m2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 3m + m2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 3m + m2 = 0 + -0.5 3m + m2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 3m + m2 = -0.5 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = -0.5 + 2.25 Reorder the terms: 2.25 + 3m + m2 = -0.5 + 2.25 Combine like terms: -0.5 + 2.25 = 1.75 2.25 + 3m + m2 = 1.75 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (m + 1.5) equal to 1.322875656 and -1.322875656.Subproblem 1
m + 1.5 = 1.322875656 Simplifying m + 1.5 = 1.322875656 Reorder the terms: 1.5 + m = 1.322875656 Solving 1.5 + m = 1.322875656 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 1.322875656 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 1.322875656 + -1.5 m = 1.322875656 + -1.5 Combine like terms: 1.322875656 + -1.5 = -0.177124344 m = -0.177124344 Simplifying m = -0.177124344Subproblem 2
m + 1.5 = -1.322875656 Simplifying m + 1.5 = -1.322875656 Reorder the terms: 1.5 + m = -1.322875656 Solving 1.5 + m = -1.322875656 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -1.322875656 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -1.322875656 + -1.5 m = -1.322875656 + -1.5 Combine like terms: -1.322875656 + -1.5 = -2.822875656 m = -2.822875656 Simplifying m = -2.822875656Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.177124344, -2.822875656}Solution
m = {-0.177124344, -2.822875656}
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