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Simplifying 2x + 3x * 7x = 42 Reorder the terms for easier multiplication: 2x + 3 * 7x * x = 42 Multiply 3 * 7 2x + 21x * x = 42 Multiply x * x 2x + 21x2 = 42 Solving 2x + 21x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 2x + 21x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 2x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -2 + 0.09523809524x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.09523809524x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.09523809524x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.09523809524x + x2 = 0 + 2 0.09523809524x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.09523809524x + x2 = 2 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 = 2 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524x + x2 = 2 + 0.002267573696 Combine like terms: 2 + 0.002267573696 = 2.002267573696 0.002267573696 + 0.09523809524x + x2 = 2.002267573696 Factor a perfect square on the left side: (x + 0.04761904762)(x + 0.04761904762) = 2.002267573696 Calculate the square root of the right side: 1.415015044 Break this problem into two subproblems by setting (x + 0.04761904762) equal to 1.415015044 and -1.415015044.Subproblem 1
x + 0.04761904762 = 1.415015044 Simplifying x + 0.04761904762 = 1.415015044 Reorder the terms: 0.04761904762 + x = 1.415015044 Solving 0.04761904762 + x = 1.415015044 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 = 1.415015044 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = 1.415015044 + -0.04761904762 x = 1.415015044 + -0.04761904762 Combine like terms: 1.415015044 + -0.04761904762 = 1.36739599638 x = 1.36739599638 Simplifying x = 1.36739599638Subproblem 2
x + 0.04761904762 = -1.415015044 Simplifying x + 0.04761904762 = -1.415015044 Reorder the terms: 0.04761904762 + x = -1.415015044 Solving 0.04761904762 + x = -1.415015044 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 = -1.415015044 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = -1.415015044 + -0.04761904762 x = -1.415015044 + -0.04761904762 Combine like terms: -1.415015044 + -0.04761904762 = -1.46263409162 x = -1.46263409162 Simplifying x = -1.46263409162Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.36739599638, -1.46263409162}
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