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Simplifying -3.6X2 + 2.3X + 3.2 = 0 Reorder the terms: 3.2 + 2.3X + -3.6X2 = 0 Solving 3.2 + 2.3X + -3.6X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -3.6 the coefficient of the squared term: Divide each side by '-3.6'. -0.8888888889 + -0.6388888889X + X2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.6388888889X + 0.8888888889 + X2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.6388888889X + X2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.6388888889X + X2 = 0 + 0.8888888889 -0.6388888889X + X2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.6388888889X + X2 = 0.8888888889 The X term is -0.6388888889X. Take half its coefficient (-0.3194444445). Square it (0.1020447531) and add it to both sides. Add '0.1020447531' to each side of the equation. -0.6388888889X + 0.1020447531 + X2 = 0.8888888889 + 0.1020447531 Reorder the terms: 0.1020447531 + -0.6388888889X + X2 = 0.8888888889 + 0.1020447531 Combine like terms: 0.8888888889 + 0.1020447531 = 0.990933642 0.1020447531 + -0.6388888889X + X2 = 0.990933642 Factor a perfect square on the left side: (X + -0.3194444445)(X + -0.3194444445) = 0.990933642 Calculate the square root of the right side: 0.995456499 Break this problem into two subproblems by setting (X + -0.3194444445) equal to 0.995456499 and -0.995456499.Subproblem 1
X + -0.3194444445 = 0.995456499 Simplifying X + -0.3194444445 = 0.995456499 Reorder the terms: -0.3194444445 + X = 0.995456499 Solving -0.3194444445 + X = 0.995456499 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3194444445' to each side of the equation. -0.3194444445 + 0.3194444445 + X = 0.995456499 + 0.3194444445 Combine like terms: -0.3194444445 + 0.3194444445 = 0.0000000000 0.0000000000 + X = 0.995456499 + 0.3194444445 X = 0.995456499 + 0.3194444445 Combine like terms: 0.995456499 + 0.3194444445 = 1.3149009435 X = 1.3149009435 Simplifying X = 1.3149009435Subproblem 2
X + -0.3194444445 = -0.995456499 Simplifying X + -0.3194444445 = -0.995456499 Reorder the terms: -0.3194444445 + X = -0.995456499 Solving -0.3194444445 + X = -0.995456499 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3194444445' to each side of the equation. -0.3194444445 + 0.3194444445 + X = -0.995456499 + 0.3194444445 Combine like terms: -0.3194444445 + 0.3194444445 = 0.0000000000 0.0000000000 + X = -0.995456499 + 0.3194444445 X = -0.995456499 + 0.3194444445 Combine like terms: -0.995456499 + 0.3194444445 = -0.6760120545 X = -0.6760120545 Simplifying X = -0.6760120545Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.3149009435, -0.6760120545}
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