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Simplifying 4m2 + -16m + -17 = -18 Reorder the terms: -17 + -16m + 4m2 = -18 Solving -17 + -16m + 4m2 = -18 Solving for variable 'm'. Reorder the terms: -17 + 18 + -16m + 4m2 = -18 + 18 Combine like terms: -17 + 18 = 1 1 + -16m + 4m2 = -18 + 18 Combine like terms: -18 + 18 = 0 1 + -16m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -4m + m2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -4m + -0.25 + m2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -4m + m2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -4m + m2 = 0 + -0.25 -4m + m2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -4m + m2 = -0.25 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = -0.25 + 4 Reorder the terms: 4 + -4m + m2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + -4m + m2 = 3.75 Factor a perfect square on the left side: (m + -2)(m + -2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (m + -2) equal to 1.936491673 and -1.936491673.Subproblem 1
m + -2 = 1.936491673 Simplifying m + -2 = 1.936491673 Reorder the terms: -2 + m = 1.936491673 Solving -2 + m = 1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + m = 1.936491673 + 2 m = 1.936491673 + 2 Combine like terms: 1.936491673 + 2 = 3.936491673 m = 3.936491673 Simplifying m = 3.936491673Subproblem 2
m + -2 = -1.936491673 Simplifying m + -2 = -1.936491673 Reorder the terms: -2 + m = -1.936491673 Solving -2 + m = -1.936491673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + m = -1.936491673 + 2 m = -1.936491673 + 2 Combine like terms: -1.936491673 + 2 = 0.063508327 m = 0.063508327 Simplifying m = 0.063508327Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.936491673, 0.063508327}
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