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Simplifying (7x + -4)(3x + 2) = 7 Reorder the terms: (-4 + 7x)(3x + 2) = 7 Reorder the terms: (-4 + 7x)(2 + 3x) = 7 Multiply (-4 + 7x) * (2 + 3x) (-4(2 + 3x) + 7x * (2 + 3x)) = 7 ((2 * -4 + 3x * -4) + 7x * (2 + 3x)) = 7 ((-8 + -12x) + 7x * (2 + 3x)) = 7 (-8 + -12x + (2 * 7x + 3x * 7x)) = 7 (-8 + -12x + (14x + 21x2)) = 7 Combine like terms: -12x + 14x = 2x (-8 + 2x + 21x2) = 7 Solving -8 + 2x + 21x2 = 7 Solving for variable 'x'. Reorder the terms: -8 + -7 + 2x + 21x2 = 7 + -7 Combine like terms: -8 + -7 = -15 -15 + 2x + 21x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -15 + 2x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.7142857143 + 0.09523809524x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.09523809524x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.09523809524x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.09523809524x + x2 = 0 + 0.7142857143 0.09523809524x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.09523809524x + x2 = 0.7142857143 The x term is 0.09523809524x. Take half its coefficient (0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. 0.09523809524x + 0.002267573696 + x2 = 0.7142857143 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524x + x2 = 0.7142857143 + 0.002267573696 Combine like terms: 0.7142857143 + 0.002267573696 = 0.716553287996 0.002267573696 + 0.09523809524x + x2 = 0.716553287996 Factor a perfect square on the left side: (x + 0.04761904762)(x + 0.04761904762) = 0.716553287996 Calculate the square root of the right side: 0.846494706 Break this problem into two subproblems by setting (x + 0.04761904762) equal to 0.846494706 and -0.846494706.Subproblem 1
x + 0.04761904762 = 0.846494706 Simplifying x + 0.04761904762 = 0.846494706 Reorder the terms: 0.04761904762 + x = 0.846494706 Solving 0.04761904762 + x = 0.846494706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = 0.846494706 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = 0.846494706 + -0.04761904762 x = 0.846494706 + -0.04761904762 Combine like terms: 0.846494706 + -0.04761904762 = 0.79887565838 x = 0.79887565838 Simplifying x = 0.79887565838Subproblem 2
x + 0.04761904762 = -0.846494706 Simplifying x + 0.04761904762 = -0.846494706 Reorder the terms: 0.04761904762 + x = -0.846494706 Solving 0.04761904762 + x = -0.846494706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = -0.846494706 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = -0.846494706 + -0.04761904762 x = -0.846494706 + -0.04761904762 Combine like terms: -0.846494706 + -0.04761904762 = -0.89411375362 x = -0.89411375362 Simplifying x = -0.89411375362Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.79887565838, -0.89411375362}
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