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Simplifying -17 + -7m = -3(2m + 7) * m Reorder the terms: -17 + -7m = -3(7 + 2m) * m Reorder the terms for easier multiplication: -17 + -7m = -3m(7 + 2m) -17 + -7m = (7 * -3m + 2m * -3m) -17 + -7m = (-21m + -6m2) Solving -17 + -7m = -21m + -6m2 Solving for variable 'm'. Combine like terms: -7m + 21m = 14m -17 + 14m + 6m2 = -21m + -6m2 + 21m + 6m2 Reorder the terms: -17 + 14m + 6m2 = -21m + 21m + -6m2 + 6m2 Combine like terms: -21m + 21m = 0 -17 + 14m + 6m2 = 0 + -6m2 + 6m2 -17 + 14m + 6m2 = -6m2 + 6m2 Combine like terms: -6m2 + 6m2 = 0 -17 + 14m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + 2.333333333m + m2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + 2.333333333m + 2.833333333 + m2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + 2.333333333m + m2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + 2.333333333m + m2 = 0 + 2.833333333 2.333333333m + m2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 2.333333333m + m2 = 2.833333333 The m term is 2.333333333m. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333m + 1.361111112 + m2 = 2.833333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333m + m2 = 2.833333333 + 1.361111112 Combine like terms: 2.833333333 + 1.361111112 = 4.194444445 1.361111112 + 2.333333333m + m2 = 4.194444445 Factor a perfect square on the left side: (m + 1.166666667)(m + 1.166666667) = 4.194444445 Calculate the square root of the right side: 2.048034288 Break this problem into two subproblems by setting (m + 1.166666667) equal to 2.048034288 and -2.048034288.Subproblem 1
m + 1.166666667 = 2.048034288 Simplifying m + 1.166666667 = 2.048034288 Reorder the terms: 1.166666667 + m = 2.048034288 Solving 1.166666667 + m = 2.048034288 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + m = 2.048034288 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + m = 2.048034288 + -1.166666667 m = 2.048034288 + -1.166666667 Combine like terms: 2.048034288 + -1.166666667 = 0.881367621 m = 0.881367621 Simplifying m = 0.881367621Subproblem 2
m + 1.166666667 = -2.048034288 Simplifying m + 1.166666667 = -2.048034288 Reorder the terms: 1.166666667 + m = -2.048034288 Solving 1.166666667 + m = -2.048034288 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + m = -2.048034288 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + m = -2.048034288 + -1.166666667 m = -2.048034288 + -1.166666667 Combine like terms: -2.048034288 + -1.166666667 = -3.214700955 m = -3.214700955 Simplifying m = -3.214700955Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.881367621, -3.214700955}
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