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Simplifying m + 5m(m + -1) = 7 Reorder the terms: m + 5m(-1 + m) = 7 m + (-1 * 5m + m * 5m) = 7 m + (-5m + 5m2) = 7 Combine like terms: m + -5m = -4m -4m + 5m2 = 7 Solving -4m + 5m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + -4m + 5m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -4m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.8m + m2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.8m + 1.4 + m2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.8m + m2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.8m + m2 = 0 + 1.4 -0.8m + m2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.8m + m2 = 1.4 The m term is -0.8m. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8m + 0.16 + m2 = 1.4 + 0.16 Reorder the terms: 0.16 + -0.8m + m2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + -0.8m + m2 = 1.56 Factor a perfect square on the left side: (m + -0.4)(m + -0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (m + -0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
m + -0.4 = 1.2489996 Simplifying m + -0.4 = 1.2489996 Reorder the terms: -0.4 + m = 1.2489996 Solving -0.4 + m = 1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = 1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = 1.2489996 + 0.4 m = 1.2489996 + 0.4 Combine like terms: 1.2489996 + 0.4 = 1.6489996 m = 1.6489996 Simplifying m = 1.6489996Subproblem 2
m + -0.4 = -1.2489996 Simplifying m + -0.4 = -1.2489996 Reorder the terms: -0.4 + m = -1.2489996 Solving -0.4 + m = -1.2489996 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + m = -1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + m = -1.2489996 + 0.4 m = -1.2489996 + 0.4 Combine like terms: -1.2489996 + 0.4 = -0.8489996 m = -0.8489996 Simplifying m = -0.8489996Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.6489996, -0.8489996}
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