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Simplifying 28x + 144 = x2 Reorder the terms: 144 + 28x = x2 Solving 144 + 28x = x2 Solving for variable 'x'. 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 = 32.439088915 x = 32.439088915 Simplifying x = 32.439088915Subproblem 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 = -4.439088915 x = -4.439088915 Simplifying x = -4.439088915Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.439088915, -4.439088915}
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