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Simplifying 10m2 = 3m + 12 Reorder the terms: 10m2 = 12 + 3m Solving 10m2 = 12 + 3m Solving for variable 'm'. Reorder the terms: -12 + -3m + 10m2 = 12 + 3m + -12 + -3m Reorder the terms: -12 + -3m + 10m2 = 12 + -12 + 3m + -3m Combine like terms: 12 + -12 = 0 -12 + -3m + 10m2 = 0 + 3m + -3m -12 + -3m + 10m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -12 + -3m + 10m2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + -0.3m + m2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.3m + 1.2 + m2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.3m + m2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.3m + m2 = 0 + 1.2 -0.3m + m2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.3m + m2 = 1.2 The m term is -0.3m. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3m + 0.0225 + m2 = 1.2 + 0.0225 Reorder the terms: 0.0225 + -0.3m + m2 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + -0.3m + m2 = 1.2225 Factor a perfect square on the left side: (m + -0.15)(m + -0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (m + -0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
m + -0.15 = 1.105667219 Simplifying m + -0.15 = 1.105667219 Reorder the terms: -0.15 + m = 1.105667219 Solving -0.15 + m = 1.105667219 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + m = 1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + m = 1.105667219 + 0.15 m = 1.105667219 + 0.15 Combine like terms: 1.105667219 + 0.15 = 1.255667219 m = 1.255667219 Simplifying m = 1.255667219Subproblem 2
m + -0.15 = -1.105667219 Simplifying m + -0.15 = -1.105667219 Reorder the terms: -0.15 + m = -1.105667219 Solving -0.15 + m = -1.105667219 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + m = -1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + m = -1.105667219 + 0.15 m = -1.105667219 + 0.15 Combine like terms: -1.105667219 + 0.15 = -0.955667219 m = -0.955667219 Simplifying m = -0.955667219Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.255667219, -0.955667219}
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