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Simplifying 6x2 + -2x = 5x + 28 Reorder the terms: -2x + 6x2 = 5x + 28 Reorder the terms: -2x + 6x2 = 28 + 5x Solving -2x + 6x2 = 28 + 5x Solving for variable 'x'. Reorder the terms: -28 + -2x + -5x + 6x2 = 28 + 5x + -28 + -5x Combine like terms: -2x + -5x = -7x -28 + -7x + 6x2 = 28 + 5x + -28 + -5x Reorder the terms: -28 + -7x + 6x2 = 28 + -28 + 5x + -5x Combine like terms: 28 + -28 = 0 -28 + -7x + 6x2 = 0 + 5x + -5x -28 + -7x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -28 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.666666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -1.166666667x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -1.166666667x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 4.666666667 -1.166666667x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -1.166666667x + x2 = 4.666666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 4.666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 4.666666667 + 0.3402777780 Combine like terms: 4.666666667 + 0.3402777780 = 5.006944445 0.3402777780 + -1.166666667x + x2 = 5.006944445 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 5.006944445 Calculate the square root of the right side: 2.237620264 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 2.237620264 and -2.237620264.Subproblem 1
x + -0.5833333335 = 2.237620264 Simplifying x + -0.5833333335 = 2.237620264 Reorder the terms: -0.5833333335 + x = 2.237620264 Solving -0.5833333335 + x = 2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 2.237620264 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 2.237620264 + 0.5833333335 x = 2.237620264 + 0.5833333335 Combine like terms: 2.237620264 + 0.5833333335 = 2.8209535975 x = 2.8209535975 Simplifying x = 2.8209535975Subproblem 2
x + -0.5833333335 = -2.237620264 Simplifying x + -0.5833333335 = -2.237620264 Reorder the terms: -0.5833333335 + x = -2.237620264 Solving -0.5833333335 + x = -2.237620264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -2.237620264 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -2.237620264 + 0.5833333335 x = -2.237620264 + 0.5833333335 Combine like terms: -2.237620264 + 0.5833333335 = -1.6542869305 x = -1.6542869305 Simplifying x = -1.6542869305Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.8209535975, -1.6542869305}
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