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Simplifying -16x2 + 68x + 0 = 72.25 Reorder the terms: 0 + 68x + -16x2 = 72.25 Remove the zero: 68x + -16x2 = 72.25 Solving 68x + -16x2 = 72.25 Solving for variable 'x'. Reorder the terms: -72.25 + 68x + -16x2 = 72.25 + -72.25 Combine like terms: 72.25 + -72.25 = 0.00 -72.25 + 68x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 4.515625 + -4.25x + x2 = 0.00 Move the constant term to the right: Add '-4.515625' to each side of the equation. 4.515625 + -4.25x + -4.515625 + x2 = 0.00 + -4.515625 Reorder the terms: 4.515625 + -4.515625 + -4.25x + x2 = 0.00 + -4.515625 Combine like terms: 4.515625 + -4.515625 = 0.000000 0.000000 + -4.25x + x2 = 0.00 + -4.515625 -4.25x + x2 = 0.00 + -4.515625 Combine like terms: 0.00 + -4.515625 = -4.515625 -4.25x + x2 = -4.515625 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -4.515625 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -4.515625 + 4.515625 Combine like terms: -4.515625 + 4.515625 = 0.000000 4.515625 + -4.25x + x2 = 0.000000 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 0.000000 Calculate the square root of the right side: 0.000000 Break this problem into two subproblems by setting (x + -2.125) equal to 0.000000 and 0.000000.Subproblem 1
x + -2.125 = 0.000000 Simplifying x + -2.125 = 0.000000 Reorder the terms: -2.125 + x = 0.000000 Solving -2.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 0.000000 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 0.000000 + 2.125 x = 0.000000 + 2.125 Combine like terms: 0.000000 + 2.125 = 2.125 x = 2.125 Simplifying x = 2.125Subproblem 2
x + -2.125 = 0.000000 Simplifying x + -2.125 = 0.000000 Reorder the terms: -2.125 + x = 0.000000 Solving -2.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 0.000000 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 0.000000 + 2.125 x = 0.000000 + 2.125 Combine like terms: 0.000000 + 2.125 = 2.125 x = 2.125 Simplifying x = 2.125Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.125, 2.125}
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