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Simplifying 144 = 28x + x2 Solving 144 = 28x + x2 Solving for variable 'x'. Reorder the terms: 144 + -28x + -1x2 = 28x + -28x + x2 + -1x2 Combine like terms: 28x + -28x = 0 144 + -28x + -1x2 = 0 + x2 + -1x2 144 + -28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + -28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 28x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 28x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 28x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 28x + x2 = 0 + 144 28x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 28x + x2 = 144 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 144 + 196 Reorder the terms: 196 + 28x + x2 = 144 + 196 Combine like terms: 144 + 196 = 340 196 + 28x + x2 = 340 Factor a perfect square on the left side: (x + 14)(x + 14) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + 14) equal to 18.439088915 and -18.439088915.Subproblem 1
x + 14 = 18.439088915 Simplifying x + 14 = 18.439088915 Reorder the terms: 14 + x = 18.439088915 Solving 14 + x = 18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 18.439088915 + -14 Combine like terms: 14 + -14 = 0 0 + x = 18.439088915 + -14 x = 18.439088915 + -14 Combine like terms: 18.439088915 + -14 = 4.439088915 x = 4.439088915 Simplifying x = 4.439088915Subproblem 2
x + 14 = -18.439088915 Simplifying x + 14 = -18.439088915 Reorder the terms: 14 + x = -18.439088915 Solving 14 + x = -18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -18.439088915 + -14 Combine like terms: 14 + -14 = 0 0 + x = -18.439088915 + -14 x = -18.439088915 + -14 Combine like terms: -18.439088915 + -14 = -32.439088915 x = -32.439088915 Simplifying x = -32.439088915Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.439088915, -32.439088915}
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