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Simplifying (6x + 7x)(4x + 7) + 5 = 2x(8x + -5) + 16 Combine like terms: 6x + 7x = 13x (13x)(4x + 7) + 5 = 2x(8x + -5) + 16 Remove parenthesis around (13x) 13x(4x + 7) + 5 = 2x(8x + -5) + 16 Reorder the terms: 13x(7 + 4x) + 5 = 2x(8x + -5) + 16 (7 * 13x + 4x * 13x) + 5 = 2x(8x + -5) + 16 (91x + 52x2) + 5 = 2x(8x + -5) + 16 Reorder the terms: 5 + 91x + 52x2 = 2x(8x + -5) + 16 Reorder the terms: 5 + 91x + 52x2 = 2x(-5 + 8x) + 16 5 + 91x + 52x2 = (-5 * 2x + 8x * 2x) + 16 5 + 91x + 52x2 = (-10x + 16x2) + 16 Reorder the terms: 5 + 91x + 52x2 = 16 + -10x + 16x2 Solving 5 + 91x + 52x2 = 16 + -10x + 16x2 Solving for variable 'x'. Reorder the terms: 5 + -16 + 91x + 10x + 52x2 + -16x2 = 16 + -10x + 16x2 + -16 + 10x + -16x2 Combine like terms: 5 + -16 = -11 -11 + 91x + 10x + 52x2 + -16x2 = 16 + -10x + 16x2 + -16 + 10x + -16x2 Combine like terms: 91x + 10x = 101x -11 + 101x + 52x2 + -16x2 = 16 + -10x + 16x2 + -16 + 10x + -16x2 Combine like terms: 52x2 + -16x2 = 36x2 -11 + 101x + 36x2 = 16 + -10x + 16x2 + -16 + 10x + -16x2 Reorder the terms: -11 + 101x + 36x2 = 16 + -16 + -10x + 10x + 16x2 + -16x2 Combine like terms: 16 + -16 = 0 -11 + 101x + 36x2 = 0 + -10x + 10x + 16x2 + -16x2 -11 + 101x + 36x2 = -10x + 10x + 16x2 + -16x2 Combine like terms: -10x + 10x = 0 -11 + 101x + 36x2 = 0 + 16x2 + -16x2 -11 + 101x + 36x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -11 + 101x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3055555556 + 2.805555556x + x2 = 0 Move the constant term to the right: Add '0.3055555556' to each side of the equation. -0.3055555556 + 2.805555556x + 0.3055555556 + x2 = 0 + 0.3055555556 Reorder the terms: -0.3055555556 + 0.3055555556 + 2.805555556x + x2 = 0 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + 2.805555556x + x2 = 0 + 0.3055555556 2.805555556x + x2 = 0 + 0.3055555556 Combine like terms: 0 + 0.3055555556 = 0.3055555556 2.805555556x + x2 = 0.3055555556 The x term is 2.805555556x. Take half its coefficient (1.402777778). Square it (1.967785494) and add it to both sides. Add '1.967785494' to each side of the equation. 2.805555556x + 1.967785494 + x2 = 0.3055555556 + 1.967785494 Reorder the terms: 1.967785494 + 2.805555556x + x2 = 0.3055555556 + 1.967785494 Combine like terms: 0.3055555556 + 1.967785494 = 2.2733410496 1.967785494 + 2.805555556x + x2 = 2.2733410496 Factor a perfect square on the left side: (x + 1.402777778)(x + 1.402777778) = 2.2733410496 Calculate the square root of the right side: 1.507760276 Break this problem into two subproblems by setting (x + 1.402777778) equal to 1.507760276 and -1.507760276.Subproblem 1
x + 1.402777778 = 1.507760276 Simplifying x + 1.402777778 = 1.507760276 Reorder the terms: 1.402777778 + x = 1.507760276 Solving 1.402777778 + x = 1.507760276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.402777778' to each side of the equation. 1.402777778 + -1.402777778 + x = 1.507760276 + -1.402777778 Combine like terms: 1.402777778 + -1.402777778 = 0.000000000 0.000000000 + x = 1.507760276 + -1.402777778 x = 1.507760276 + -1.402777778 Combine like terms: 1.507760276 + -1.402777778 = 0.104982498 x = 0.104982498 Simplifying x = 0.104982498Subproblem 2
x + 1.402777778 = -1.507760276 Simplifying x + 1.402777778 = -1.507760276 Reorder the terms: 1.402777778 + x = -1.507760276 Solving 1.402777778 + x = -1.507760276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.402777778' to each side of the equation. 1.402777778 + -1.402777778 + x = -1.507760276 + -1.402777778 Combine like terms: 1.402777778 + -1.402777778 = 0.000000000 0.000000000 + x = -1.507760276 + -1.402777778 x = -1.507760276 + -1.402777778 Combine like terms: -1.507760276 + -1.402777778 = -2.910538054 x = -2.910538054 Simplifying x = -2.910538054Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.104982498, -2.910538054}
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