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Simplifying 12x2 + -29x + 8 = 0 Reorder the terms: 8 + -29x + 12x2 = 0 Solving 8 + -29x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.6666666667 + -2.416666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.416666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.416666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.416666667x + x2 = 0 + -0.6666666667 -2.416666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.416666667x + x2 = -0.6666666667 The x term is -2.416666667x. Take half its coefficient (-1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. -2.416666667x + 1.460069446 + x2 = -0.6666666667 + 1.460069446 Reorder the terms: 1.460069446 + -2.416666667x + x2 = -0.6666666667 + 1.460069446 Combine like terms: -0.6666666667 + 1.460069446 = 0.7934027793 1.460069446 + -2.416666667x + x2 = 0.7934027793 Factor a perfect square on the left side: (x + -1.208333334)(x + -1.208333334) = 0.7934027793 Calculate the square root of the right side: 0.890731598 Break this problem into two subproblems by setting (x + -1.208333334) equal to 0.890731598 and -0.890731598.Subproblem 1
x + -1.208333334 = 0.890731598 Simplifying x + -1.208333334 = 0.890731598 Reorder the terms: -1.208333334 + x = 0.890731598 Solving -1.208333334 + x = 0.890731598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = 0.890731598 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = 0.890731598 + 1.208333334 x = 0.890731598 + 1.208333334 Combine like terms: 0.890731598 + 1.208333334 = 2.099064932 x = 2.099064932 Simplifying x = 2.099064932Subproblem 2
x + -1.208333334 = -0.890731598 Simplifying x + -1.208333334 = -0.890731598 Reorder the terms: -1.208333334 + x = -0.890731598 Solving -1.208333334 + x = -0.890731598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = -0.890731598 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = -0.890731598 + 1.208333334 x = -0.890731598 + 1.208333334 Combine like terms: -0.890731598 + 1.208333334 = 0.317601736 x = 0.317601736 Simplifying x = 0.317601736Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.099064932, 0.317601736}
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