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Simplifying (9x + 7)(3x + -1) = 49 + -1x2 Reorder the terms: (7 + 9x)(3x + -1) = 49 + -1x2 Reorder the terms: (7 + 9x)(-1 + 3x) = 49 + -1x2 Multiply (7 + 9x) * (-1 + 3x) (7(-1 + 3x) + 9x * (-1 + 3x)) = 49 + -1x2 ((-1 * 7 + 3x * 7) + 9x * (-1 + 3x)) = 49 + -1x2 ((-7 + 21x) + 9x * (-1 + 3x)) = 49 + -1x2 (-7 + 21x + (-1 * 9x + 3x * 9x)) = 49 + -1x2 (-7 + 21x + (-9x + 27x2)) = 49 + -1x2 Combine like terms: 21x + -9x = 12x (-7 + 12x + 27x2) = 49 + -1x2 Solving -7 + 12x + 27x2 = 49 + -1x2 Solving for variable 'x'. Reorder the terms: -7 + -49 + 12x + 27x2 + x2 = 49 + -1x2 + -49 + x2 Combine like terms: -7 + -49 = -56 -56 + 12x + 27x2 + x2 = 49 + -1x2 + -49 + x2 Combine like terms: 27x2 + x2 = 28x2 -56 + 12x + 28x2 = 49 + -1x2 + -49 + x2 Reorder the terms: -56 + 12x + 28x2 = 49 + -49 + -1x2 + x2 Combine like terms: 49 + -49 = 0 -56 + 12x + 28x2 = 0 + -1x2 + x2 -56 + 12x + 28x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -56 + 12x + 28x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 3x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying -14 + 3x + 7x2 = 0 Solving -14 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.4285714286x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.4285714286x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.4285714286x + x2 = 0 + 2 0.4285714286x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.4285714286x + x2 = 2 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 = 2 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 2 + 0.04591836735 Combine like terms: 2 + 0.04591836735 = 2.04591836735 0.04591836735 + 0.4285714286x + x2 = 2.04591836735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 2.04591836735 Calculate the square root of the right side: 1.430356028 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.430356028 and -1.430356028.Subproblem 1
x + 0.2142857143 = 1.430356028 Simplifying x + 0.2142857143 = 1.430356028 Reorder the terms: 0.2142857143 + x = 1.430356028 Solving 0.2142857143 + x = 1.430356028 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 = 1.430356028 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.430356028 + -0.2142857143 x = 1.430356028 + -0.2142857143 Combine like terms: 1.430356028 + -0.2142857143 = 1.2160703137 x = 1.2160703137 Simplifying x = 1.2160703137Subproblem 2
x + 0.2142857143 = -1.430356028 Simplifying x + 0.2142857143 = -1.430356028 Reorder the terms: 0.2142857143 + x = -1.430356028 Solving 0.2142857143 + x = -1.430356028 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 = -1.430356028 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.430356028 + -0.2142857143 x = -1.430356028 + -0.2142857143 Combine like terms: -1.430356028 + -0.2142857143 = -1.6446417423 x = -1.6446417423 Simplifying x = -1.6446417423Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2160703137, -1.6446417423}Solution
x = {1.2160703137, -1.6446417423}
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