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Simplifying 133 = (2x + 10)(x + 1) Reorder the terms: 133 = (10 + 2x)(x + 1) Reorder the terms: 133 = (10 + 2x)(1 + x) Multiply (10 + 2x) * (1 + x) 133 = (10(1 + x) + 2x * (1 + x)) 133 = ((1 * 10 + x * 10) + 2x * (1 + x)) 133 = ((10 + 10x) + 2x * (1 + x)) 133 = (10 + 10x + (1 * 2x + x * 2x)) 133 = (10 + 10x + (2x + 2x2)) Combine like terms: 10x + 2x = 12x 133 = (10 + 12x + 2x2) Solving 133 = 10 + 12x + 2x2 Solving for variable 'x'. Combine like terms: 133 + -10 = 123 123 + -12x + -2x2 = 10 + 12x + 2x2 + -10 + -12x + -2x2 Reorder the terms: 123 + -12x + -2x2 = 10 + -10 + 12x + -12x + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 123 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 123 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 123 + -12x + -2x2 = 0 + 2x2 + -2x2 123 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 123 + -12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -61.5 + 6x + x2 = 0 Move the constant term to the right: Add '61.5' to each side of the equation. -61.5 + 6x + 61.5 + x2 = 0 + 61.5 Reorder the terms: -61.5 + 61.5 + 6x + x2 = 0 + 61.5 Combine like terms: -61.5 + 61.5 = 0.0 0.0 + 6x + x2 = 0 + 61.5 6x + x2 = 0 + 61.5 Combine like terms: 0 + 61.5 = 61.5 6x + x2 = 61.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 61.5 + 9 Reorder the terms: 9 + 6x + x2 = 61.5 + 9 Combine like terms: 61.5 + 9 = 70.5 9 + 6x + x2 = 70.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 70.5 Calculate the square root of the right side: 8.396427812 Break this problem into two subproblems by setting (x + 3) equal to 8.396427812 and -8.396427812.Subproblem 1
x + 3 = 8.396427812 Simplifying x + 3 = 8.396427812 Reorder the terms: 3 + x = 8.396427812 Solving 3 + x = 8.396427812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.396427812 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.396427812 + -3 x = 8.396427812 + -3 Combine like terms: 8.396427812 + -3 = 5.396427812 x = 5.396427812 Simplifying x = 5.396427812Subproblem 2
x + 3 = -8.396427812 Simplifying x + 3 = -8.396427812 Reorder the terms: 3 + x = -8.396427812 Solving 3 + x = -8.396427812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.396427812 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.396427812 + -3 x = -8.396427812 + -3 Combine like terms: -8.396427812 + -3 = -11.396427812 x = -11.396427812 Simplifying x = -11.396427812Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.396427812, -11.396427812}
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