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Simplifying 12x2 + 29x = 2 Reorder the terms: 29x + 12x2 = 2 Solving 29x + 12x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 29x + 12x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 29x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.1666666667 + 2.416666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 2.416666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 2.416666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 2.416666667x + x2 = 0 + 0.1666666667 2.416666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 2.416666667x + x2 = 0.1666666667 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 = 0.1666666667 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667x + x2 = 0.1666666667 + 1.460069446 Combine like terms: 0.1666666667 + 1.460069446 = 1.6267361127 1.460069446 + 2.416666667x + x2 = 1.6267361127 Factor a perfect square on the left side: (x + 1.208333334)(x + 1.208333334) = 1.6267361127 Calculate the square root of the right side: 1.275435656 Break this problem into two subproblems by setting (x + 1.208333334) equal to 1.275435656 and -1.275435656.Subproblem 1
x + 1.208333334 = 1.275435656 Simplifying x + 1.208333334 = 1.275435656 Reorder the terms: 1.208333334 + x = 1.275435656 Solving 1.208333334 + x = 1.275435656 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 = 1.275435656 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = 1.275435656 + -1.208333334 x = 1.275435656 + -1.208333334 Combine like terms: 1.275435656 + -1.208333334 = 0.067102322 x = 0.067102322 Simplifying x = 0.067102322Subproblem 2
x + 1.208333334 = -1.275435656 Simplifying x + 1.208333334 = -1.275435656 Reorder the terms: 1.208333334 + x = -1.275435656 Solving 1.208333334 + x = -1.275435656 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 = -1.275435656 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = -1.275435656 + -1.208333334 x = -1.275435656 + -1.208333334 Combine like terms: -1.275435656 + -1.208333334 = -2.48376899 x = -2.48376899 Simplifying x = -2.48376899Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.067102322, -2.48376899}
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