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Simplifying 8x2 + -6x = 7x2 + 6x + -2 Reorder the terms: -6x + 8x2 = 7x2 + 6x + -2 Reorder the terms: -6x + 8x2 = -2 + 6x + 7x2 Solving -6x + 8x2 = -2 + 6x + 7x2 Solving for variable 'x'. Reorder the terms: 2 + -6x + -6x + 8x2 + -7x2 = -2 + 6x + 7x2 + 2 + -6x + -7x2 Combine like terms: -6x + -6x = -12x 2 + -12x + 8x2 + -7x2 = -2 + 6x + 7x2 + 2 + -6x + -7x2 Combine like terms: 8x2 + -7x2 = 1x2 2 + -12x + 1x2 = -2 + 6x + 7x2 + 2 + -6x + -7x2 Reorder the terms: 2 + -12x + 1x2 = -2 + 2 + 6x + -6x + 7x2 + -7x2 Combine like terms: -2 + 2 = 0 2 + -12x + 1x2 = 0 + 6x + -6x + 7x2 + -7x2 2 + -12x + 1x2 = 6x + -6x + 7x2 + -7x2 Combine like terms: 6x + -6x = 0 2 + -12x + 1x2 = 0 + 7x2 + -7x2 2 + -12x + 1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 2 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -12x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -12x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -12x + x2 = 0 + -2 -12x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -12x + x2 = -2 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -2 + 36 Reorder the terms: 36 + -12x + x2 = -2 + 36 Combine like terms: -2 + 36 = 34 36 + -12x + x2 = 34 Factor a perfect square on the left side: (x + -6)(x + -6) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -6) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -6 = 5.830951895 Simplifying x + -6 = 5.830951895 Reorder the terms: -6 + x = 5.830951895 Solving -6 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.830951895 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.830951895 + 6 x = 5.830951895 + 6 Combine like terms: 5.830951895 + 6 = 11.830951895 x = 11.830951895 Simplifying x = 11.830951895Subproblem 2
x + -6 = -5.830951895 Simplifying x + -6 = -5.830951895 Reorder the terms: -6 + x = -5.830951895 Solving -6 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.830951895 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.830951895 + 6 x = -5.830951895 + 6 Combine like terms: -5.830951895 + 6 = 0.169048105 x = 0.169048105 Simplifying x = 0.169048105Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.830951895, 0.169048105}
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