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Simplifying 4m(4m) + 2m = 11 Remove parenthesis around (4m) 4m * 4m + 2m = 11 Reorder the terms for easier multiplication: 4 * 4m * m + 2m = 11 Multiply 4 * 4 16m * m + 2m = 11 Multiply m * m 16m2 + 2m = 11 Reorder the terms: 2m + 16m2 = 11 Solving 2m + 16m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + 2m + 16m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 2m + 16m2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.6875 + 0.125m + m2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + 0.125m + 0.6875 + m2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + 0.125m + m2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + 0.125m + m2 = 0 + 0.6875 0.125m + m2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 0.125m + m2 = 0.6875 The m term is 0.125m. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125m + 0.00390625 + m2 = 0.6875 + 0.00390625 Reorder the terms: 0.00390625 + 0.125m + m2 = 0.6875 + 0.00390625 Combine like terms: 0.6875 + 0.00390625 = 0.69140625 0.00390625 + 0.125m + m2 = 0.69140625 Factor a perfect square on the left side: (m + 0.0625)(m + 0.0625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (m + 0.0625) equal to 0.831508418 and -0.831508418.Subproblem 1
m + 0.0625 = 0.831508418 Simplifying m + 0.0625 = 0.831508418 Reorder the terms: 0.0625 + m = 0.831508418 Solving 0.0625 + m = 0.831508418 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + m = 0.831508418 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + m = 0.831508418 + -0.0625 m = 0.831508418 + -0.0625 Combine like terms: 0.831508418 + -0.0625 = 0.769008418 m = 0.769008418 Simplifying m = 0.769008418Subproblem 2
m + 0.0625 = -0.831508418 Simplifying m + 0.0625 = -0.831508418 Reorder the terms: 0.0625 + m = -0.831508418 Solving 0.0625 + m = -0.831508418 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + m = -0.831508418 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + m = -0.831508418 + -0.0625 m = -0.831508418 + -0.0625 Combine like terms: -0.831508418 + -0.0625 = -0.894008418 m = -0.894008418 Simplifying m = -0.894008418Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.769008418, -0.894008418}
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