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Simplifying (x + 3)(x + 3) = (7x + 1)(x + -1) Reorder the terms: (3 + x)(x + 3) = (7x + 1)(x + -1) Reorder the terms: (3 + x)(3 + x) = (7x + 1)(x + -1) Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) = (7x + 1)(x + -1) ((3 * 3 + x * 3) + x(3 + x)) = (7x + 1)(x + -1) ((9 + 3x) + x(3 + x)) = (7x + 1)(x + -1) (9 + 3x + (3 * x + x * x)) = (7x + 1)(x + -1) (9 + 3x + (3x + x2)) = (7x + 1)(x + -1) Combine like terms: 3x + 3x = 6x (9 + 6x + x2) = (7x + 1)(x + -1) Reorder the terms: 9 + 6x + x2 = (1 + 7x)(x + -1) Reorder the terms: 9 + 6x + x2 = (1 + 7x)(-1 + x) Multiply (1 + 7x) * (-1 + x) 9 + 6x + x2 = (1(-1 + x) + 7x * (-1 + x)) 9 + 6x + x2 = ((-1 * 1 + x * 1) + 7x * (-1 + x)) 9 + 6x + x2 = ((-1 + 1x) + 7x * (-1 + x)) 9 + 6x + x2 = (-1 + 1x + (-1 * 7x + x * 7x)) 9 + 6x + x2 = (-1 + 1x + (-7x + 7x2)) Combine like terms: 1x + -7x = -6x 9 + 6x + x2 = (-1 + -6x + 7x2) Solving 9 + 6x + x2 = -1 + -6x + 7x2 Solving for variable 'x'. Reorder the terms: 9 + 1 + 6x + 6x + x2 + -7x2 = -1 + -6x + 7x2 + 1 + 6x + -7x2 Combine like terms: 9 + 1 = 10 10 + 6x + 6x + x2 + -7x2 = -1 + -6x + 7x2 + 1 + 6x + -7x2 Combine like terms: 6x + 6x = 12x 10 + 12x + x2 + -7x2 = -1 + -6x + 7x2 + 1 + 6x + -7x2 Combine like terms: x2 + -7x2 = -6x2 10 + 12x + -6x2 = -1 + -6x + 7x2 + 1 + 6x + -7x2 Reorder the terms: 10 + 12x + -6x2 = -1 + 1 + -6x + 6x + 7x2 + -7x2 Combine like terms: -1 + 1 = 0 10 + 12x + -6x2 = 0 + -6x + 6x + 7x2 + -7x2 10 + 12x + -6x2 = -6x + 6x + 7x2 + -7x2 Combine like terms: -6x + 6x = 0 10 + 12x + -6x2 = 0 + 7x2 + -7x2 10 + 12x + -6x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 10 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 6x + -3x2)' equal to zero and attempt to solve: Simplifying 5 + 6x + -3x2 = 0 Solving 5 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -2x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -2x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.666666667 -2x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -2x + x2 = 1.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 1.666666667 + 1 Combine like terms: 1.666666667 + 1 = 2.666666667 1 + -2x + x2 = 2.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (x + -1) equal to 1.632993162 and -1.632993162.Subproblem 1
x + -1 = 1.632993162 Simplifying x + -1 = 1.632993162 Reorder the terms: -1 + x = 1.632993162 Solving -1 + x = 1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.632993162 + 1 x = 1.632993162 + 1 Combine like terms: 1.632993162 + 1 = 2.632993162 x = 2.632993162 Simplifying x = 2.632993162Subproblem 2
x + -1 = -1.632993162 Simplifying x + -1 = -1.632993162 Reorder the terms: -1 + x = -1.632993162 Solving -1 + x = -1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.632993162 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.632993162 + 1 x = -1.632993162 + 1 Combine like terms: -1.632993162 + 1 = -0.632993162 x = -0.632993162 Simplifying x = -0.632993162Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.632993162, -0.632993162}Solution
x = {2.632993162, -0.632993162}
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