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Simplifying 11X2 + -4.6X + -7.3 = 0 Reorder the terms: -7.3 + -4.6X + 11X2 = 0 Solving -7.3 + -4.6X + 11X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6636363636 + -0.4181818182X + X2 = 0 Move the constant term to the right: Add '0.6636363636' to each side of the equation. -0.6636363636 + -0.4181818182X + 0.6636363636 + X2 = 0 + 0.6636363636 Reorder the terms: -0.6636363636 + 0.6636363636 + -0.4181818182X + X2 = 0 + 0.6636363636 Combine like terms: -0.6636363636 + 0.6636363636 = 0.0000000000 0.0000000000 + -0.4181818182X + X2 = 0 + 0.6636363636 -0.4181818182X + X2 = 0 + 0.6636363636 Combine like terms: 0 + 0.6636363636 = 0.6636363636 -0.4181818182X + X2 = 0.6636363636 The X term is -0.4181818182X. Take half its coefficient (-0.2090909091). Square it (0.04371900827) and add it to both sides. Add '0.04371900827' to each side of the equation. -0.4181818182X + 0.04371900827 + X2 = 0.6636363636 + 0.04371900827 Reorder the terms: 0.04371900827 + -0.4181818182X + X2 = 0.6636363636 + 0.04371900827 Combine like terms: 0.6636363636 + 0.04371900827 = 0.70735537187 0.04371900827 + -0.4181818182X + X2 = 0.70735537187 Factor a perfect square on the left side: (X + -0.2090909091)(X + -0.2090909091) = 0.70735537187 Calculate the square root of the right side: 0.841044215 Break this problem into two subproblems by setting (X + -0.2090909091) equal to 0.841044215 and -0.841044215.Subproblem 1
X + -0.2090909091 = 0.841044215 Simplifying X + -0.2090909091 = 0.841044215 Reorder the terms: -0.2090909091 + X = 0.841044215 Solving -0.2090909091 + X = 0.841044215 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2090909091' to each side of the equation. -0.2090909091 + 0.2090909091 + X = 0.841044215 + 0.2090909091 Combine like terms: -0.2090909091 + 0.2090909091 = 0.0000000000 0.0000000000 + X = 0.841044215 + 0.2090909091 X = 0.841044215 + 0.2090909091 Combine like terms: 0.841044215 + 0.2090909091 = 1.0501351241 X = 1.0501351241 Simplifying X = 1.0501351241Subproblem 2
X + -0.2090909091 = -0.841044215 Simplifying X + -0.2090909091 = -0.841044215 Reorder the terms: -0.2090909091 + X = -0.841044215 Solving -0.2090909091 + X = -0.841044215 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2090909091' to each side of the equation. -0.2090909091 + 0.2090909091 + X = -0.841044215 + 0.2090909091 Combine like terms: -0.2090909091 + 0.2090909091 = 0.0000000000 0.0000000000 + X = -0.841044215 + 0.2090909091 X = -0.841044215 + 0.2090909091 Combine like terms: -0.841044215 + 0.2090909091 = -0.6319533059 X = -0.6319533059 Simplifying X = -0.6319533059Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.0501351241, -0.6319533059}
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