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Simplifying 8m2 + -16m + -35 = 0 Reorder the terms: -35 + -16m + 8m2 = 0 Solving -35 + -16m + 8m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -2m + m2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -2m + 4.375 + m2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -2m + m2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -2m + m2 = 0 + 4.375 -2m + m2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -2m + m2 = 4.375 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 = 4.375 + 1 Reorder the terms: 1 + -2m + m2 = 4.375 + 1 Combine like terms: 4.375 + 1 = 5.375 1 + -2m + m2 = 5.375 Factor a perfect square on the left side: (m + -1)(m + -1) = 5.375 Calculate the square root of the right side: 2.318404624 Break this problem into two subproblems by setting (m + -1) equal to 2.318404624 and -2.318404624.Subproblem 1
m + -1 = 2.318404624 Simplifying m + -1 = 2.318404624 Reorder the terms: -1 + m = 2.318404624 Solving -1 + m = 2.318404624 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 = 2.318404624 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.318404624 + 1 m = 2.318404624 + 1 Combine like terms: 2.318404624 + 1 = 3.318404624 m = 3.318404624 Simplifying m = 3.318404624Subproblem 2
m + -1 = -2.318404624 Simplifying m + -1 = -2.318404624 Reorder the terms: -1 + m = -2.318404624 Solving -1 + m = -2.318404624 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 = -2.318404624 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.318404624 + 1 m = -2.318404624 + 1 Combine like terms: -2.318404624 + 1 = -1.318404624 m = -1.318404624 Simplifying m = -1.318404624Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.318404624, -1.318404624}
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