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Simplifying m * m + m = 960 Multiply m * m m2 + m = 960 Reorder the terms: m + m2 = 960 Solving m + m2 = 960 Solving for variable 'm'. Reorder the terms: -960 + m + m2 = 960 + -960 Combine like terms: 960 + -960 = 0 -960 + m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '960' to each side of the equation. -960 + m + 960 + m2 = 0 + 960 Reorder the terms: -960 + 960 + m + m2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + m + m2 = 0 + 960 m + m2 = 0 + 960 Combine like terms: 0 + 960 = 960 m + m2 = 960 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = 960 + 0.25 Reorder the terms: 0.25 + m + m2 = 960 + 0.25 Combine like terms: 960 + 0.25 = 960.25 0.25 + m + m2 = 960.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 960.25 Calculate the square root of the right side: 30.987900865 Break this problem into two subproblems by setting (m + 0.5) equal to 30.987900865 and -30.987900865.Subproblem 1
m + 0.5 = 30.987900865 Simplifying m + 0.5 = 30.987900865 Reorder the terms: 0.5 + m = 30.987900865 Solving 0.5 + m = 30.987900865 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 30.987900865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 30.987900865 + -0.5 m = 30.987900865 + -0.5 Combine like terms: 30.987900865 + -0.5 = 30.487900865 m = 30.487900865 Simplifying m = 30.487900865Subproblem 2
m + 0.5 = -30.987900865 Simplifying m + 0.5 = -30.987900865 Reorder the terms: 0.5 + m = -30.987900865 Solving 0.5 + m = -30.987900865 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -30.987900865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -30.987900865 + -0.5 m = -30.987900865 + -0.5 Combine like terms: -30.987900865 + -0.5 = -31.487900865 m = -31.487900865 Simplifying m = -31.487900865Solution
The solution to the problem is based on the solutions from the subproblems. m = {30.487900865, -31.487900865}
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