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Simplifying 6x(x + 12) = 5 + -1x Reorder the terms: 6x(12 + x) = 5 + -1x (12 * 6x + x * 6x) = 5 + -1x (72x + 6x2) = 5 + -1x Solving 72x + 6x2 = 5 + -1x Solving for variable 'x'. Reorder the terms: -5 + 72x + x + 6x2 = 5 + -1x + -5 + x Combine like terms: 72x + x = 73x -5 + 73x + 6x2 = 5 + -1x + -5 + x Reorder the terms: -5 + 73x + 6x2 = 5 + -5 + -1x + x Combine like terms: 5 + -5 = 0 -5 + 73x + 6x2 = 0 + -1x + x -5 + 73x + 6x2 = -1x + x Combine like terms: -1x + x = 0 -5 + 73x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + 12.16666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 12.16666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 12.16666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 12.16666667x + x2 = 0 + 0.8333333333 12.16666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 12.16666667x + x2 = 0.8333333333 The x term is 12.16666667x. Take half its coefficient (6.083333335). Square it (37.00694446) and add it to both sides. Add '37.00694446' to each side of the equation. 12.16666667x + 37.00694446 + x2 = 0.8333333333 + 37.00694446 Reorder the terms: 37.00694446 + 12.16666667x + x2 = 0.8333333333 + 37.00694446 Combine like terms: 0.8333333333 + 37.00694446 = 37.8402777933 37.00694446 + 12.16666667x + x2 = 37.8402777933 Factor a perfect square on the left side: (x + 6.083333335)(x + 6.083333335) = 37.8402777933 Calculate the square root of the right side: 6.151445179 Break this problem into two subproblems by setting (x + 6.083333335) equal to 6.151445179 and -6.151445179.Subproblem 1
x + 6.083333335 = 6.151445179 Simplifying x + 6.083333335 = 6.151445179 Reorder the terms: 6.083333335 + x = 6.151445179 Solving 6.083333335 + x = 6.151445179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.083333335' to each side of the equation. 6.083333335 + -6.083333335 + x = 6.151445179 + -6.083333335 Combine like terms: 6.083333335 + -6.083333335 = 0.000000000 0.000000000 + x = 6.151445179 + -6.083333335 x = 6.151445179 + -6.083333335 Combine like terms: 6.151445179 + -6.083333335 = 0.068111844 x = 0.068111844 Simplifying x = 0.068111844Subproblem 2
x + 6.083333335 = -6.151445179 Simplifying x + 6.083333335 = -6.151445179 Reorder the terms: 6.083333335 + x = -6.151445179 Solving 6.083333335 + x = -6.151445179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.083333335' to each side of the equation. 6.083333335 + -6.083333335 + x = -6.151445179 + -6.083333335 Combine like terms: 6.083333335 + -6.083333335 = 0.000000000 0.000000000 + x = -6.151445179 + -6.083333335 x = -6.151445179 + -6.083333335 Combine like terms: -6.151445179 + -6.083333335 = -12.234778514 x = -12.234778514 Simplifying x = -12.234778514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.068111844, -12.234778514}
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