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Simplifying X2 + -12X + -4.5 = 0 Reorder the terms: -4.5 + -12X + X2 = 0 Solving -4.5 + -12X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -12X + 4.5 + X2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -12X + X2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -12X + X2 = 0 + 4.5 -12X + X2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -12X + X2 = 4.5 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = 4.5 + 36 Reorder the terms: 36 + -12X + X2 = 4.5 + 36 Combine like terms: 4.5 + 36 = 40.5 36 + -12X + X2 = 40.5 Factor a perfect square on the left side: (X + -6)(X + -6) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (X + -6) equal to 6.363961031 and -6.363961031.Subproblem 1
X + -6 = 6.363961031 Simplifying X + -6 = 6.363961031 Reorder the terms: -6 + X = 6.363961031 Solving -6 + X = 6.363961031 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 6.363961031 + 6 Combine like terms: -6 + 6 = 0 0 + X = 6.363961031 + 6 X = 6.363961031 + 6 Combine like terms: 6.363961031 + 6 = 12.363961031 X = 12.363961031 Simplifying X = 12.363961031Subproblem 2
X + -6 = -6.363961031 Simplifying X + -6 = -6.363961031 Reorder the terms: -6 + X = -6.363961031 Solving -6 + X = -6.363961031 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -6.363961031 + 6 Combine like terms: -6 + 6 = 0 0 + X = -6.363961031 + 6 X = -6.363961031 + 6 Combine like terms: -6.363961031 + 6 = -0.363961031 X = -0.363961031 Simplifying X = -0.363961031Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.363961031, -0.363961031}
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