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Simplifying 19.14 + x2 + 8x = 144 Reorder the terms: 19.14 + 8x + x2 = 144 Solving 19.14 + 8x + x2 = 144 Solving for variable 'x'. Reorder the terms: 19.14 + -144 + 8x + x2 = 144 + -144 Combine like terms: 19.14 + -144 = -124.86 -124.86 + 8x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -124.86 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124.86' to each side of the equation. -124.86 + 8x + 124.86 + x2 = 0 + 124.86 Reorder the terms: -124.86 + 124.86 + 8x + x2 = 0 + 124.86 Combine like terms: -124.86 + 124.86 = 0.00 0.00 + 8x + x2 = 0 + 124.86 8x + x2 = 0 + 124.86 Combine like terms: 0 + 124.86 = 124.86 8x + x2 = 124.86 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 124.86 + 16 Reorder the terms: 16 + 8x + x2 = 124.86 + 16 Combine like terms: 124.86 + 16 = 140.86 16 + 8x + x2 = 140.86 Factor a perfect square on the left side: (x + 4)(x + 4) = 140.86 Calculate the square root of the right side: 11.86844556 Break this problem into two subproblems by setting (x + 4) equal to 11.86844556 and -11.86844556.Subproblem 1
x + 4 = 11.86844556 Simplifying x + 4 = 11.86844556 Reorder the terms: 4 + x = 11.86844556 Solving 4 + x = 11.86844556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 11.86844556 + -4 Combine like terms: 4 + -4 = 0 0 + x = 11.86844556 + -4 x = 11.86844556 + -4 Combine like terms: 11.86844556 + -4 = 7.86844556 x = 7.86844556 Simplifying x = 7.86844556Subproblem 2
x + 4 = -11.86844556 Simplifying x + 4 = -11.86844556 Reorder the terms: 4 + x = -11.86844556 Solving 4 + x = -11.86844556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -11.86844556 + -4 Combine like terms: 4 + -4 = 0 0 + x = -11.86844556 + -4 x = -11.86844556 + -4 Combine like terms: -11.86844556 + -4 = -15.86844556 x = -15.86844556 Simplifying x = -15.86844556Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.86844556, -15.86844556}
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