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Simplifying 4m2 + 4m + -23 = 0 Reorder the terms: -23 + 4m + 4m2 = 0 Solving -23 + 4m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + m + m2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + m + 5.75 + m2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + m + m2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + m + m2 = 0 + 5.75 m + m2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 m + m2 = 5.75 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. + 0.25 + m2 = 5.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 5.75 + 0.25 Combine like terms: 5.75 + 0.25 = 6 1.25 + m2 = 6 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m + 0.5) equal to 2.449489743 and -2.449489743.Subproblem 1
m + 0.5 = 2.449489743 Simplifying m + 0.5 = 2.449489743 Reorder the terms: 0.5 + m = 2.449489743 Solving 0.5 + m = 2.449489743 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 = 2.449489743 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 2.449489743 + -0.5 m = 2.449489743 + -0.5 Combine like terms: 2.449489743 + -0.5 = 1.949489743 m = 1.949489743 Simplifying m = 1.949489743Subproblem 2
m + 0.5 = -2.449489743 Simplifying m + 0.5 = -2.449489743 Reorder the terms: 0.5 + m = -2.449489743 Solving 0.5 + m = -2.449489743 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 = -2.449489743 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -2.449489743 + -0.5 m = -2.449489743 + -0.5 Combine like terms: -2.449489743 + -0.5 = -2.949489743 m = -2.949489743 Simplifying m = -2.949489743Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.949489743, -2.949489743}
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