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Simplifying 4.25 = -16x2 + 68x Reorder the terms: 4.25 = 68x + -16x2 Solving 4.25 = 68x + -16x2 Solving for variable 'x'. Reorder the terms: 4.25 + -68x + 16x2 = 68x + -68x + -16x2 + 16x2 Combine like terms: 68x + -68x = 0 4.25 + -68x + 16x2 = 0 + -16x2 + 16x2 4.25 + -68x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4.25 + -68x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.265625 + -4.25x + x2 = 0 Move the constant term to the right: Add '-0.265625' to each side of the equation. 0.265625 + -4.25x + -0.265625 + x2 = 0 + -0.265625 Reorder the terms: 0.265625 + -0.265625 + -4.25x + x2 = 0 + -0.265625 Combine like terms: 0.265625 + -0.265625 = 0.000000 0.000000 + -4.25x + x2 = 0 + -0.265625 -4.25x + x2 = 0 + -0.265625 Combine like terms: 0 + -0.265625 = -0.265625 -4.25x + x2 = -0.265625 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 = -0.265625 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -0.265625 + 4.515625 Combine like terms: -0.265625 + 4.515625 = 4.25 4.515625 + -4.25x + x2 = 4.25 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -2.125) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -2.125 = 2.061552813 Simplifying x + -2.125 = 2.061552813 Reorder the terms: -2.125 + x = 2.061552813 Solving -2.125 + x = 2.061552813 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 = 2.061552813 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 2.061552813 + 2.125 x = 2.061552813 + 2.125 Combine like terms: 2.061552813 + 2.125 = 4.186552813 x = 4.186552813 Simplifying x = 4.186552813Subproblem 2
x + -2.125 = -2.061552813 Simplifying x + -2.125 = -2.061552813 Reorder the terms: -2.125 + x = -2.061552813 Solving -2.125 + x = -2.061552813 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 = -2.061552813 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -2.061552813 + 2.125 x = -2.061552813 + 2.125 Combine like terms: -2.061552813 + 2.125 = 0.063447187 x = 0.063447187 Simplifying x = 0.063447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.186552813, 0.063447187}
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