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Simplifying 4m2 + 16m + 9 = 0 Reorder the terms: 9 + 16m + 4m2 = 0 Solving 9 + 16m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 4m + m2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 4m + -2.25 + m2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 4m + m2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 4m + m2 = 0 + -2.25 4m + m2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 4m + m2 = -2.25 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 = -2.25 + 4 Reorder the terms: 4 + 4m + m2 = -2.25 + 4 Combine like terms: -2.25 + 4 = 1.75 4 + 4m + m2 = 1.75 Factor a perfect square on the left side: (m + 2)(m + 2) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (m + 2) equal to 1.322875656 and -1.322875656.Subproblem 1
m + 2 = 1.322875656 Simplifying m + 2 = 1.322875656 Reorder the terms: 2 + m = 1.322875656 Solving 2 + m = 1.322875656 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 = 1.322875656 + -2 Combine like terms: 2 + -2 = 0 0 + m = 1.322875656 + -2 m = 1.322875656 + -2 Combine like terms: 1.322875656 + -2 = -0.677124344 m = -0.677124344 Simplifying m = -0.677124344Subproblem 2
m + 2 = -1.322875656 Simplifying m + 2 = -1.322875656 Reorder the terms: 2 + m = -1.322875656 Solving 2 + m = -1.322875656 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 = -1.322875656 + -2 Combine like terms: 2 + -2 = 0 0 + m = -1.322875656 + -2 m = -1.322875656 + -2 Combine like terms: -1.322875656 + -2 = -3.322875656 m = -3.322875656 Simplifying m = -3.322875656Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.677124344, -3.322875656}
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