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Simplifying 7 + -7x = (3x + 2)(x + 1) Reorder the terms: 7 + -7x = (2 + 3x)(x + 1) Reorder the terms: 7 + -7x = (2 + 3x)(1 + x) Multiply (2 + 3x) * (1 + x) 7 + -7x = (2(1 + x) + 3x * (1 + x)) 7 + -7x = ((1 * 2 + x * 2) + 3x * (1 + x)) 7 + -7x = ((2 + 2x) + 3x * (1 + x)) 7 + -7x = (2 + 2x + (1 * 3x + x * 3x)) 7 + -7x = (2 + 2x + (3x + 3x2)) Combine like terms: 2x + 3x = 5x 7 + -7x = (2 + 5x + 3x2) Solving 7 + -7x = 2 + 5x + 3x2 Solving for variable 'x'. Reorder the terms: 7 + -2 + -7x + -5x + -3x2 = 2 + 5x + 3x2 + -2 + -5x + -3x2 Combine like terms: 7 + -2 = 5 5 + -7x + -5x + -3x2 = 2 + 5x + 3x2 + -2 + -5x + -3x2 Combine like terms: -7x + -5x = -12x 5 + -12x + -3x2 = 2 + 5x + 3x2 + -2 + -5x + -3x2 Reorder the terms: 5 + -12x + -3x2 = 2 + -2 + 5x + -5x + 3x2 + -3x2 Combine like terms: 2 + -2 = 0 5 + -12x + -3x2 = 0 + 5x + -5x + 3x2 + -3x2 5 + -12x + -3x2 = 5x + -5x + 3x2 + -3x2 Combine like terms: 5x + -5x = 0 5 + -12x + -3x2 = 0 + 3x2 + -3x2 5 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + -12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 4x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 4x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.666666667 4x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 4x + x2 = 1.666666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.666666667 + 4 Reorder the terms: 4 + 4x + x2 = 1.666666667 + 4 Combine like terms: 1.666666667 + 4 = 5.666666667 4 + 4x + x2 = 5.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.666666667 Calculate the square root of the right side: 2.380476143 Break this problem into two subproblems by setting (x + 2) equal to 2.380476143 and -2.380476143.Subproblem 1
x + 2 = 2.380476143 Simplifying x + 2 = 2.380476143 Reorder the terms: 2 + x = 2.380476143 Solving 2 + x = 2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.380476143 + -2 x = 2.380476143 + -2 Combine like terms: 2.380476143 + -2 = 0.380476143 x = 0.380476143 Simplifying x = 0.380476143Subproblem 2
x + 2 = -2.380476143 Simplifying x + 2 = -2.380476143 Reorder the terms: 2 + x = -2.380476143 Solving 2 + x = -2.380476143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.380476143 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.380476143 + -2 x = -2.380476143 + -2 Combine like terms: -2.380476143 + -2 = -4.380476143 x = -4.380476143 Simplifying x = -4.380476143Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.380476143, -4.380476143}
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