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Simplifying 7x(3x + 3) + x = 2x + 17 Reorder the terms: 7x(3 + 3x) + x = 2x + 17 (3 * 7x + 3x * 7x) + x = 2x + 17 (21x + 21x2) + x = 2x + 17 Reorder the terms: 21x + x + 21x2 = 2x + 17 Combine like terms: 21x + x = 22x 22x + 21x2 = 2x + 17 Reorder the terms: 22x + 21x2 = 17 + 2x Solving 22x + 21x2 = 17 + 2x Solving for variable 'x'. Reorder the terms: -17 + 22x + -2x + 21x2 = 17 + 2x + -17 + -2x Combine like terms: 22x + -2x = 20x -17 + 20x + 21x2 = 17 + 2x + -17 + -2x Reorder the terms: -17 + 20x + 21x2 = 17 + -17 + 2x + -2x Combine like terms: 17 + -17 = 0 -17 + 20x + 21x2 = 0 + 2x + -2x -17 + 20x + 21x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -17 + 20x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.8095238095 + 0.9523809524x + x2 = 0 Move the constant term to the right: Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.9523809524x + 0.8095238095 + x2 = 0 + 0.8095238095 Reorder the terms: -0.8095238095 + 0.8095238095 + 0.9523809524x + x2 = 0 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + 0.9523809524x + x2 = 0 + 0.8095238095 0.9523809524x + x2 = 0 + 0.8095238095 Combine like terms: 0 + 0.8095238095 = 0.8095238095 0.9523809524x + x2 = 0.8095238095 The x term is 0.9523809524x. Take half its coefficient (0.4761904762). Square it (0.2267573696) and add it to both sides. Add '0.2267573696' to each side of the equation. 0.9523809524x + 0.2267573696 + x2 = 0.8095238095 + 0.2267573696 Reorder the terms: 0.2267573696 + 0.9523809524x + x2 = 0.8095238095 + 0.2267573696 Combine like terms: 0.8095238095 + 0.2267573696 = 1.0362811791 0.2267573696 + 0.9523809524x + x2 = 1.0362811791 Factor a perfect square on the left side: (x + 0.4761904762)(x + 0.4761904762) = 1.0362811791 Calculate the square root of the right side: 1.017978968 Break this problem into two subproblems by setting (x + 0.4761904762) equal to 1.017978968 and -1.017978968.Subproblem 1
x + 0.4761904762 = 1.017978968 Simplifying x + 0.4761904762 = 1.017978968 Reorder the terms: 0.4761904762 + x = 1.017978968 Solving 0.4761904762 + x = 1.017978968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4761904762' to each side of the equation. 0.4761904762 + -0.4761904762 + x = 1.017978968 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + x = 1.017978968 + -0.4761904762 x = 1.017978968 + -0.4761904762 Combine like terms: 1.017978968 + -0.4761904762 = 0.5417884918 x = 0.5417884918 Simplifying x = 0.5417884918Subproblem 2
x + 0.4761904762 = -1.017978968 Simplifying x + 0.4761904762 = -1.017978968 Reorder the terms: 0.4761904762 + x = -1.017978968 Solving 0.4761904762 + x = -1.017978968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4761904762' to each side of the equation. 0.4761904762 + -0.4761904762 + x = -1.017978968 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + x = -1.017978968 + -0.4761904762 x = -1.017978968 + -0.4761904762 Combine like terms: -1.017978968 + -0.4761904762 = -1.4941694442 x = -1.4941694442 Simplifying x = -1.4941694442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5417884918, -1.4941694442}
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