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Simplifying 8m2 + 16m + -43 = 4 Reorder the terms: -43 + 16m + 8m2 = 4 Solving -43 + 16m + 8m2 = 4 Solving for variable 'm'. Reorder the terms: -43 + -4 + 16m + 8m2 = 4 + -4 Combine like terms: -43 + -4 = -47 -47 + 16m + 8m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -47 + 16m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.875 + 2m + m2 = 0 Move the constant term to the right: Add '5.875' to each side of the equation. -5.875 + 2m + 5.875 + m2 = 0 + 5.875 Reorder the terms: -5.875 + 5.875 + 2m + m2 = 0 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + 2m + m2 = 0 + 5.875 2m + m2 = 0 + 5.875 Combine like terms: 0 + 5.875 = 5.875 2m + m2 = 5.875 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 = 5.875 + 1 Reorder the terms: 1 + 2m + m2 = 5.875 + 1 Combine like terms: 5.875 + 1 = 6.875 1 + 2m + m2 = 6.875 Factor a perfect square on the left side: (m + 1)(m + 1) = 6.875 Calculate the square root of the right side: 2.62202212 Break this problem into two subproblems by setting (m + 1) equal to 2.62202212 and -2.62202212.Subproblem 1
m + 1 = 2.62202212 Simplifying m + 1 = 2.62202212 Reorder the terms: 1 + m = 2.62202212 Solving 1 + m = 2.62202212 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 = 2.62202212 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.62202212 + -1 m = 2.62202212 + -1 Combine like terms: 2.62202212 + -1 = 1.62202212 m = 1.62202212 Simplifying m = 1.62202212Subproblem 2
m + 1 = -2.62202212 Simplifying m + 1 = -2.62202212 Reorder the terms: 1 + m = -2.62202212 Solving 1 + m = -2.62202212 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 = -2.62202212 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.62202212 + -1 m = -2.62202212 + -1 Combine like terms: -2.62202212 + -1 = -3.62202212 m = -3.62202212 Simplifying m = -3.62202212Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.62202212, -3.62202212}
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