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Simplifying -9m2 + 11m + -2 + 4m2 + -8m + 7 = 0 Reorder the terms: -2 + 7 + 11m + -8m + -9m2 + 4m2 = 0 Combine like terms: -2 + 7 = 5 5 + 11m + -8m + -9m2 + 4m2 = 0 Combine like terms: 11m + -8m = 3m 5 + 3m + -9m2 + 4m2 = 0 Combine like terms: -9m2 + 4m2 = -5m2 5 + 3m + -5m2 = 0 Solving 5 + 3m + -5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + -0.6m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.6m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -0.6m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.6m + m2 = 0 + 1 -0.6m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.6m + m2 = 1 The m term is -0.6m. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6m + 0.09 + m2 = 1 + 0.09 Reorder the terms: 0.09 + -0.6m + m2 = 1 + 0.09 Combine like terms: 1 + 0.09 = 1.09 0.09 + -0.6m + m2 = 1.09 Factor a perfect square on the left side: (m + -0.3)(m + -0.3) = 1.09 Calculate the square root of the right side: 1.044030651 Break this problem into two subproblems by setting (m + -0.3) equal to 1.044030651 and -1.044030651.Subproblem 1
m + -0.3 = 1.044030651 Simplifying m + -0.3 = 1.044030651 Reorder the terms: -0.3 + m = 1.044030651 Solving -0.3 + m = 1.044030651 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + m = 1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + m = 1.044030651 + 0.3 m = 1.044030651 + 0.3 Combine like terms: 1.044030651 + 0.3 = 1.344030651 m = 1.344030651 Simplifying m = 1.344030651Subproblem 2
m + -0.3 = -1.044030651 Simplifying m + -0.3 = -1.044030651 Reorder the terms: -0.3 + m = -1.044030651 Solving -0.3 + m = -1.044030651 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + m = -1.044030651 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + m = -1.044030651 + 0.3 m = -1.044030651 + 0.3 Combine like terms: -1.044030651 + 0.3 = -0.744030651 m = -0.744030651 Simplifying m = -0.744030651Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.344030651, -0.744030651}
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