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Simplifying 8x6 + 195x3 + -27 = 0 Reorder the terms: -27 + 195x3 + 8x6 = 0 Solving -27 + 195x3 + 8x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.375 + 24.375x3 + x6 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 24.375x3 + 3.375 + x6 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 24.375x3 + x6 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 24.375x3 + x6 = 0 + 3.375 24.375x3 + x6 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 24.375x3 + x6 = 3.375 The x term is 24.375x3. Take half its coefficient (12.1875). Square it (148.5351563) and add it to both sides. Add '148.5351563' to each side of the equation. 24.375x3 + 148.5351563 + x6 = 3.375 + 148.5351563 Reorder the terms: 148.5351563 + 24.375x3 + x6 = 3.375 + 148.5351563 Combine like terms: 3.375 + 148.5351563 = 151.9101563 148.5351563 + 24.375x3 + x6 = 151.9101563 Factor a perfect square on the left side: (x3 + 12.1875)(x3 + 12.1875) = 151.9101563 Calculate the square root of the right side: 12.325183824 Break this problem into two subproblems by setting (x3 + 12.1875) equal to 12.325183824 and -12.325183824.Subproblem 1
x3 + 12.1875 = 12.325183824 Simplifying x3 + 12.1875 = 12.325183824 Reorder the terms: 12.1875 + x3 = 12.325183824 Solving 12.1875 + x3 = 12.325183824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.1875' to each side of the equation. 12.1875 + -12.1875 + x3 = 12.325183824 + -12.1875 Combine like terms: 12.1875 + -12.1875 = 0.0000 0.0000 + x3 = 12.325183824 + -12.1875 x3 = 12.325183824 + -12.1875 Combine like terms: 12.325183824 + -12.1875 = 0.137683824 x3 = 0.137683824 Simplifying x3 = 0.137683824 Reorder the terms: -0.137683824 + x3 = 0.137683824 + -0.137683824 Combine like terms: 0.137683824 + -0.137683824 = 0.000000000 -0.137683824 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 12.1875 = -12.325183824 Simplifying x3 + 12.1875 = -12.325183824 Reorder the terms: 12.1875 + x3 = -12.325183824 Solving 12.1875 + x3 = -12.325183824 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.1875' to each side of the equation. 12.1875 + -12.1875 + x3 = -12.325183824 + -12.1875 Combine like terms: 12.1875 + -12.1875 = 0.0000 0.0000 + x3 = -12.325183824 + -12.1875 x3 = -12.325183824 + -12.1875 Combine like terms: -12.325183824 + -12.1875 = -24.512683824 x3 = -24.512683824 Simplifying x3 = -24.512683824 Reorder the terms: 24.512683824 + x3 = -24.512683824 + 24.512683824 Combine like terms: -24.512683824 + 24.512683824 = 0.000000000 24.512683824 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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