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Simplifying 6(x + -9) * x = 7(x + -8) + 2 Reorder the terms: 6(-9 + x) * x = 7(x + -8) + 2 Reorder the terms for easier multiplication: 6x(-9 + x) = 7(x + -8) + 2 (-9 * 6x + x * 6x) = 7(x + -8) + 2 (-54x + 6x2) = 7(x + -8) + 2 Reorder the terms: -54x + 6x2 = 7(-8 + x) + 2 -54x + 6x2 = (-8 * 7 + x * 7) + 2 -54x + 6x2 = (-56 + 7x) + 2 Reorder the terms: -54x + 6x2 = -56 + 2 + 7x Combine like terms: -56 + 2 = -54 -54x + 6x2 = -54 + 7x Solving -54x + 6x2 = -54 + 7x Solving for variable 'x'. Reorder the terms: 54 + -54x + -7x + 6x2 = -54 + 7x + 54 + -7x Combine like terms: -54x + -7x = -61x 54 + -61x + 6x2 = -54 + 7x + 54 + -7x Reorder the terms: 54 + -61x + 6x2 = -54 + 54 + 7x + -7x Combine like terms: -54 + 54 = 0 54 + -61x + 6x2 = 0 + 7x + -7x 54 + -61x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 54 + -61x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 9 + -10.16666667x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -10.16666667x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -10.16666667x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10.16666667x + x2 = 0 + -9 -10.16666667x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -10.16666667x + x2 = -9 The x term is -10.16666667x. Take half its coefficient (-5.083333335). Square it (25.84027779) and add it to both sides. Add '25.84027779' to each side of the equation. -10.16666667x + 25.84027779 + x2 = -9 + 25.84027779 Reorder the terms: 25.84027779 + -10.16666667x + x2 = -9 + 25.84027779 Combine like terms: -9 + 25.84027779 = 16.84027779 25.84027779 + -10.16666667x + x2 = 16.84027779 Factor a perfect square on the left side: (x + -5.083333335)(x + -5.083333335) = 16.84027779 Calculate the square root of the right side: 4.103690752 Break this problem into two subproblems by setting (x + -5.083333335) equal to 4.103690752 and -4.103690752.Subproblem 1
x + -5.083333335 = 4.103690752 Simplifying x + -5.083333335 = 4.103690752 Reorder the terms: -5.083333335 + x = 4.103690752 Solving -5.083333335 + x = 4.103690752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.083333335' to each side of the equation. -5.083333335 + 5.083333335 + x = 4.103690752 + 5.083333335 Combine like terms: -5.083333335 + 5.083333335 = 0.000000000 0.000000000 + x = 4.103690752 + 5.083333335 x = 4.103690752 + 5.083333335 Combine like terms: 4.103690752 + 5.083333335 = 9.187024087 x = 9.187024087 Simplifying x = 9.187024087Subproblem 2
x + -5.083333335 = -4.103690752 Simplifying x + -5.083333335 = -4.103690752 Reorder the terms: -5.083333335 + x = -4.103690752 Solving -5.083333335 + x = -4.103690752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.083333335' to each side of the equation. -5.083333335 + 5.083333335 + x = -4.103690752 + 5.083333335 Combine like terms: -5.083333335 + 5.083333335 = 0.000000000 0.000000000 + x = -4.103690752 + 5.083333335 x = -4.103690752 + 5.083333335 Combine like terms: -4.103690752 + 5.083333335 = 0.979642583 x = 0.979642583 Simplifying x = 0.979642583Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.187024087, 0.979642583}
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