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Simplifying 2m2 + -4m + -3 = 0 Reorder the terms: -3 + -4m + 2m2 = 0 Solving -3 + -4m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -2m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2m + m2 = 0 + 1.5 -2m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2m + m2 = 1.5 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 = 1.5 + 1 Reorder the terms: 1 + -2m + m2 = 1.5 + 1 Combine like terms: 1.5 + 1 = 2.5 1 + -2m + m2 = 2.5 Factor a perfect square on the left side: (m + -1)(m + -1) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (m + -1) equal to 1.58113883 and -1.58113883.Subproblem 1
m + -1 = 1.58113883 Simplifying m + -1 = 1.58113883 Reorder the terms: -1 + m = 1.58113883 Solving -1 + m = 1.58113883 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 = 1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.58113883 + 1 m = 1.58113883 + 1 Combine like terms: 1.58113883 + 1 = 2.58113883 m = 2.58113883 Simplifying m = 2.58113883Subproblem 2
m + -1 = -1.58113883 Simplifying m + -1 = -1.58113883 Reorder the terms: -1 + m = -1.58113883 Solving -1 + m = -1.58113883 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 = -1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.58113883 + 1 m = -1.58113883 + 1 Combine like terms: -1.58113883 + 1 = -0.58113883 m = -0.58113883 Simplifying m = -0.58113883Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.58113883, -0.58113883}
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