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Simplifying 120 + 26x + x2 = 144 Solving 120 + 26x + x2 = 144 Solving for variable 'x'. Reorder the terms: 120 + -144 + 26x + x2 = 144 + -144 Combine like terms: 120 + -144 = -24 -24 + 26x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -24 + 26x + x2 = 0 Begin completing the square. 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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