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Simplifying 2m2 + -18m + 15 = 0 Reorder the terms: 15 + -18m + 2m2 = 0 Solving 15 + -18m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -9m + m2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -9m + -7.5 + m2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -9m + m2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -9m + m2 = 0 + -7.5 -9m + m2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -9m + m2 = -7.5 The m term is -9m. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9m + 20.25 + m2 = -7.5 + 20.25 Reorder the terms: 20.25 + -9m + m2 = -7.5 + 20.25 Combine like terms: -7.5 + 20.25 = 12.75 20.25 + -9m + m2 = 12.75 Factor a perfect square on the left side: (m + -4.5)(m + -4.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (m + -4.5) equal to 3.570714214 and -3.570714214.Subproblem 1
m + -4.5 = 3.570714214 Simplifying m + -4.5 = 3.570714214 Reorder the terms: -4.5 + m = 3.570714214 Solving -4.5 + m = 3.570714214 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = 3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = 3.570714214 + 4.5 m = 3.570714214 + 4.5 Combine like terms: 3.570714214 + 4.5 = 8.070714214 m = 8.070714214 Simplifying m = 8.070714214Subproblem 2
m + -4.5 = -3.570714214 Simplifying m + -4.5 = -3.570714214 Reorder the terms: -4.5 + m = -3.570714214 Solving -4.5 + m = -3.570714214 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = -3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = -3.570714214 + 4.5 m = -3.570714214 + 4.5 Combine like terms: -3.570714214 + 4.5 = 0.929285786 m = 0.929285786 Simplifying m = 0.929285786Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.070714214, 0.929285786}
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