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Simplifying (7x + 3)(4x) = 36 Reorder the terms: (3 + 7x)(4x) = 36 Remove parenthesis around (4x) (3 + 7x) * 4x = 36 Reorder the terms for easier multiplication: 4x(3 + 7x) = 36 (3 * 4x + 7x * 4x) = 36 (12x + 28x2) = 36 Solving 12x + 28x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 12x + 28x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 12x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + 3x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying -9 + 3x + 7x2 = 0 Solving -9 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 0.4285714286x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 0.4285714286x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 1.285714286 0.4285714286x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 0.4285714286x + x2 = 1.285714286 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 = 1.285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 1.285714286 + 0.04591836735 Combine like terms: 1.285714286 + 0.04591836735 = 1.33163265335 0.04591836735 + 0.4285714286x + x2 = 1.33163265335 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 1.33163265335 Calculate the square root of the right side: 1.153963887 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.153963887 and -1.153963887.Subproblem 1
x + 0.2142857143 = 1.153963887 Simplifying x + 0.2142857143 = 1.153963887 Reorder the terms: 0.2142857143 + x = 1.153963887 Solving 0.2142857143 + x = 1.153963887 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 = 1.153963887 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.153963887 + -0.2142857143 x = 1.153963887 + -0.2142857143 Combine like terms: 1.153963887 + -0.2142857143 = 0.9396781727 x = 0.9396781727 Simplifying x = 0.9396781727Subproblem 2
x + 0.2142857143 = -1.153963887 Simplifying x + 0.2142857143 = -1.153963887 Reorder the terms: 0.2142857143 + x = -1.153963887 Solving 0.2142857143 + x = -1.153963887 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 = -1.153963887 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.153963887 + -0.2142857143 x = -1.153963887 + -0.2142857143 Combine like terms: -1.153963887 + -0.2142857143 = -1.3682496013 x = -1.3682496013 Simplifying x = -1.3682496013Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9396781727, -1.3682496013}Solution
x = {0.9396781727, -1.3682496013}
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