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Simplifying (7x + 3)(4x) = 35 Reorder the terms: (3 + 7x)(4x) = 35 Remove parenthesis around (4x) (3 + 7x) * 4x = 35 Reorder the terms for easier multiplication: 4x(3 + 7x) = 35 (3 * 4x + 7x * 4x) = 35 (12x + 28x2) = 35 Solving 12x + 28x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 12x + 28x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 12x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -1.25 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.4285714286x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.4285714286x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.4285714286x + x2 = 0 + 1.25 0.4285714286x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.4285714286x + x2 = 1.25 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 1.25 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1.25 + 0.04591836735 Combine like terms: 1.25 + 0.04591836735 = 1.29591836735 0.04591836735 + 0.4285714286x + x2 = 1.29591836735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.29591836735 Calculate the square root of the right side: 1.138384104 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.138384104 and -1.138384104.Subproblem 1
x + 0.2142857143 = 1.138384104 Simplifying x + 0.2142857143 = 1.138384104 Reorder the terms: 0.2142857143 + x = 1.138384104 Solving 0.2142857143 + x = 1.138384104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.138384104 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.138384104 + -0.2142857143 x = 1.138384104 + -0.2142857143 Combine like terms: 1.138384104 + -0.2142857143 = 0.9240983897 x = 0.9240983897 Simplifying x = 0.9240983897Subproblem 2
x + 0.2142857143 = -1.138384104 Simplifying x + 0.2142857143 = -1.138384104 Reorder the terms: 0.2142857143 + x = -1.138384104 Solving 0.2142857143 + x = -1.138384104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.138384104 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.138384104 + -0.2142857143 x = -1.138384104 + -0.2142857143 Combine like terms: -1.138384104 + -0.2142857143 = -1.3526698183 x = -1.3526698183 Simplifying x = -1.3526698183Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9240983897, -1.3526698183}
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