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Simplifying -16x2 + 80x + 5 = 26 Reorder the terms: 5 + 80x + -16x2 = 26 Solving 5 + 80x + -16x2 = 26 Solving for variable 'x'. Reorder the terms: 5 + -26 + 80x + -16x2 = 26 + -26 Combine like terms: 5 + -26 = -21 -21 + 80x + -16x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -21 + 80x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.3125 + -5x + x2 = 0 Move the constant term to the right: Add '-1.3125' to each side of the equation. 1.3125 + -5x + -1.3125 + x2 = 0 + -1.3125 Reorder the terms: 1.3125 + -1.3125 + -5x + x2 = 0 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + -5x + x2 = 0 + -1.3125 -5x + x2 = 0 + -1.3125 Combine like terms: 0 + -1.3125 = -1.3125 -5x + x2 = -1.3125 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.3125 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.3125 + 6.25 Combine like terms: -1.3125 + 6.25 = 4.9375 6.25 + -5x + x2 = 4.9375 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (x + -2.5) equal to 2.222048604 and -2.222048604.Subproblem 1
x + -2.5 = 2.222048604 Simplifying x + -2.5 = 2.222048604 Reorder the terms: -2.5 + x = 2.222048604 Solving -2.5 + x = 2.222048604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.222048604 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.222048604 + 2.5 x = 2.222048604 + 2.5 Combine like terms: 2.222048604 + 2.5 = 4.722048604 x = 4.722048604 Simplifying x = 4.722048604Subproblem 2
x + -2.5 = -2.222048604 Simplifying x + -2.5 = -2.222048604 Reorder the terms: -2.5 + x = -2.222048604 Solving -2.5 + x = -2.222048604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.222048604 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.222048604 + 2.5 x = -2.222048604 + 2.5 Combine like terms: -2.222048604 + 2.5 = 0.277951396 x = 0.277951396 Simplifying x = 0.277951396Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.722048604, 0.277951396}
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