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Simplifying 144 = (6 + x)(20 + x) Multiply (6 + x) * (20 + x) 144 = (6(20 + x) + x(20 + x)) 144 = ((20 * 6 + x * 6) + x(20 + x)) 144 = ((120 + 6x) + x(20 + x)) 144 = (120 + 6x + (20 * x + x * x)) 144 = (120 + 6x + (20x + x2)) Combine like terms: 6x + 20x = 26x 144 = (120 + 26x + x2) Solving 144 = 120 + 26x + x2 Solving for variable 'x'. Combine like terms: 144 + -120 = 24 24 + -26x + -1x2 = 120 + 26x + x2 + -120 + -26x + -1x2 Reorder the terms: 24 + -26x + -1x2 = 120 + -120 + 26x + -26x + x2 + -1x2 Combine like terms: 120 + -120 = 0 24 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2 24 + -26x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 24 + -26x + -1x2 = 0 + x2 + -1x2 24 + -26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + -26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 26x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 26x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 26x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 26x + x2 = 0 + 24 26x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 26x + x2 = 24 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 24 + 169 Reorder the terms: 169 + 26x + x2 = 24 + 169 Combine like terms: 24 + 169 = 193 169 + 26x + x2 = 193 Factor a perfect square on the left side: (x + 13)(x + 13) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (x + 13) equal to 13.892443989 and -13.892443989.Subproblem 1
x + 13 = 13.892443989 Simplifying x + 13 = 13.892443989 Reorder the terms: 13 + x = 13.892443989 Solving 13 + x = 13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 13.892443989 + -13 Combine like terms: 13 + -13 = 0 0 + x = 13.892443989 + -13 x = 13.892443989 + -13 Combine like terms: 13.892443989 + -13 = 0.892443989 x = 0.892443989 Simplifying x = 0.892443989Subproblem 2
x + 13 = -13.892443989 Simplifying x + 13 = -13.892443989 Reorder the terms: 13 + x = -13.892443989 Solving 13 + x = -13.892443989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -13.892443989 + -13 Combine like terms: 13 + -13 = 0 0 + x = -13.892443989 + -13 x = -13.892443989 + -13 Combine like terms: -13.892443989 + -13 = -26.892443989 x = -26.892443989 Simplifying x = -26.892443989Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.892443989, -26.892443989}
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