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Simplifying 7m2 = 9(3 + m) 7m2 = (3 * 9 + m * 9) 7m2 = (27 + 9m) Solving 7m2 = 27 + 9m Solving for variable 'm'. Reorder the terms: -27 + -9m + 7m2 = 27 + 9m + -27 + -9m Reorder the terms: -27 + -9m + 7m2 = 27 + -27 + 9m + -9m Combine like terms: 27 + -27 = 0 -27 + -9m + 7m2 = 0 + 9m + -9m -27 + -9m + 7m2 = 9m + -9m Combine like terms: 9m + -9m = 0 -27 + -9m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.857142857 + -1.285714286m + m2 = 0 Move the constant term to the right: Add '3.857142857' to each side of the equation. -3.857142857 + -1.285714286m + 3.857142857 + m2 = 0 + 3.857142857 Reorder the terms: -3.857142857 + 3.857142857 + -1.285714286m + m2 = 0 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + -1.285714286m + m2 = 0 + 3.857142857 -1.285714286m + m2 = 0 + 3.857142857 Combine like terms: 0 + 3.857142857 = 3.857142857 -1.285714286m + m2 = 3.857142857 The m term is -1.285714286m. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286m + 0.4132653063 + m2 = 3.857142857 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286m + m2 = 3.857142857 + 0.4132653063 Combine like terms: 3.857142857 + 0.4132653063 = 4.2704081633 0.4132653063 + -1.285714286m + m2 = 4.2704081633 Factor a perfect square on the left side: (m + -0.642857143)(m + -0.642857143) = 4.2704081633 Calculate the square root of the right side: 2.066496592 Break this problem into two subproblems by setting (m + -0.642857143) equal to 2.066496592 and -2.066496592.Subproblem 1
m + -0.642857143 = 2.066496592 Simplifying m + -0.642857143 = 2.066496592 Reorder the terms: -0.642857143 + m = 2.066496592 Solving -0.642857143 + m = 2.066496592 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + m = 2.066496592 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + m = 2.066496592 + 0.642857143 m = 2.066496592 + 0.642857143 Combine like terms: 2.066496592 + 0.642857143 = 2.709353735 m = 2.709353735 Simplifying m = 2.709353735Subproblem 2
m + -0.642857143 = -2.066496592 Simplifying m + -0.642857143 = -2.066496592 Reorder the terms: -0.642857143 + m = -2.066496592 Solving -0.642857143 + m = -2.066496592 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + m = -2.066496592 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + m = -2.066496592 + 0.642857143 m = -2.066496592 + 0.642857143 Combine like terms: -2.066496592 + 0.642857143 = -1.423639449 m = -1.423639449 Simplifying m = -1.423639449Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.709353735, -1.423639449}
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