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Simplifying 10m2 + -15m + -28 = 0 Reorder the terms: -28 + -15m + 10m2 = 0 Solving -28 + -15m + 10m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.8 + -1.5m + m2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1.5m + 2.8 + m2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1.5m + m2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1.5m + m2 = 0 + 2.8 -1.5m + m2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -1.5m + m2 = 2.8 The m term is -1.5m. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5m + 0.5625 + m2 = 2.8 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 2.8 + 0.5625 Combine like terms: 2.8 + 0.5625 = 3.3625 0.5625 + -1.5m + m2 = 3.3625 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 3.3625 Calculate the square root of the right side: 1.833712082 Break this problem into two subproblems by setting (m + -0.75) equal to 1.833712082 and -1.833712082.Subproblem 1
m + -0.75 = 1.833712082 Simplifying m + -0.75 = 1.833712082 Reorder the terms: -0.75 + m = 1.833712082 Solving -0.75 + m = 1.833712082 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 1.833712082 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 1.833712082 + 0.75 m = 1.833712082 + 0.75 Combine like terms: 1.833712082 + 0.75 = 2.583712082 m = 2.583712082 Simplifying m = 2.583712082Subproblem 2
m + -0.75 = -1.833712082 Simplifying m + -0.75 = -1.833712082 Reorder the terms: -0.75 + m = -1.833712082 Solving -0.75 + m = -1.833712082 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -1.833712082 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -1.833712082 + 0.75 m = -1.833712082 + 0.75 Combine like terms: -1.833712082 + 0.75 = -1.083712082 m = -1.083712082 Simplifying m = -1.083712082Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.583712082, -1.083712082}
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