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Simplifying x + 2x(6x + 2) = 29 Reorder the terms: x + 2x(2 + 6x) = 29 x + (2 * 2x + 6x * 2x) = 29 x + (4x + 12x2) = 29 Combine like terms: x + 4x = 5x 5x + 12x2 = 29 Solving 5x + 12x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 5x + 12x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.416666667 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '2.416666667' to each side of the equation. -2.416666667 + 0.4166666667x + 2.416666667 + x2 = 0 + 2.416666667 Reorder the terms: -2.416666667 + 2.416666667 + 0.4166666667x + x2 = 0 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + 0.4166666667x + x2 = 0 + 2.416666667 0.4166666667x + x2 = 0 + 2.416666667 Combine like terms: 0 + 2.416666667 = 2.416666667 0.4166666667x + x2 = 2.416666667 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 2.416666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 2.416666667 + 0.04340277781 Combine like terms: 2.416666667 + 0.04340277781 = 2.46006944481 0.04340277781 + 0.4166666667x + x2 = 2.46006944481 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 2.46006944481 Calculate the square root of the right side: 1.568460852 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 1.568460852 and -1.568460852.Subproblem 1
x + 0.2083333334 = 1.568460852 Simplifying x + 0.2083333334 = 1.568460852 Reorder the terms: 0.2083333334 + x = 1.568460852 Solving 0.2083333334 + x = 1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 1.568460852 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 1.568460852 + -0.2083333334 x = 1.568460852 + -0.2083333334 Combine like terms: 1.568460852 + -0.2083333334 = 1.3601275186 x = 1.3601275186 Simplifying x = 1.3601275186Subproblem 2
x + 0.2083333334 = -1.568460852 Simplifying x + 0.2083333334 = -1.568460852 Reorder the terms: 0.2083333334 + x = -1.568460852 Solving 0.2083333334 + x = -1.568460852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -1.568460852 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -1.568460852 + -0.2083333334 x = -1.568460852 + -0.2083333334 Combine like terms: -1.568460852 + -0.2083333334 = -1.7767941854 x = -1.7767941854 Simplifying x = -1.7767941854Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3601275186, -1.7767941854}
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