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Simplifying 5m2 + 12m + 3 = 0 Reorder the terms: 3 + 12m + 5m2 = 0 Solving 3 + 12m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 2.4m + m2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 2.4m + -0.6 + m2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 2.4m + m2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 2.4m + m2 = 0 + -0.6 2.4m + m2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 2.4m + m2 = -0.6 The m term is 2.4m. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4m + 1.44 + m2 = -0.6 + 1.44 Reorder the terms: 1.44 + 2.4m + m2 = -0.6 + 1.44 Combine like terms: -0.6 + 1.44 = 0.84 1.44 + 2.4m + m2 = 0.84 Factor a perfect square on the left side: (m + 1.2)(m + 1.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (m + 1.2) equal to 0.916515139 and -0.916515139.Subproblem 1
m + 1.2 = 0.916515139 Simplifying m + 1.2 = 0.916515139 Reorder the terms: 1.2 + m = 0.916515139 Solving 1.2 + m = 0.916515139 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + m = 0.916515139 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + m = 0.916515139 + -1.2 m = 0.916515139 + -1.2 Combine like terms: 0.916515139 + -1.2 = -0.283484861 m = -0.283484861 Simplifying m = -0.283484861Subproblem 2
m + 1.2 = -0.916515139 Simplifying m + 1.2 = -0.916515139 Reorder the terms: 1.2 + m = -0.916515139 Solving 1.2 + m = -0.916515139 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + m = -0.916515139 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + m = -0.916515139 + -1.2 m = -0.916515139 + -1.2 Combine like terms: -0.916515139 + -1.2 = -2.116515139 m = -2.116515139 Simplifying m = -2.116515139Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.283484861, -2.116515139}
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