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Simplifying -16x2 + 65x + 5 = 0 Reorder the terms: 5 + 65x + -16x2 = 0 Solving 5 + 65x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -4.0625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.0625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.0625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.0625x + x2 = 0 + 0.3125 -4.0625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.0625x + x2 = 0.3125 The x term is -4.0625x. Take half its coefficient (-2.03125). Square it (4.125976563) and add it to both sides. Add '4.125976563' to each side of the equation. -4.0625x + 4.125976563 + x2 = 0.3125 + 4.125976563 Reorder the terms: 4.125976563 + -4.0625x + x2 = 0.3125 + 4.125976563 Combine like terms: 0.3125 + 4.125976563 = 4.438476563 4.125976563 + -4.0625x + x2 = 4.438476563 Factor a perfect square on the left side: (x + -2.03125)(x + -2.03125) = 4.438476563 Calculate the square root of the right side: 2.106769224 Break this problem into two subproblems by setting (x + -2.03125) equal to 2.106769224 and -2.106769224.Subproblem 1
x + -2.03125 = 2.106769224 Simplifying x + -2.03125 = 2.106769224 Reorder the terms: -2.03125 + x = 2.106769224 Solving -2.03125 + x = 2.106769224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + x = 2.106769224 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + x = 2.106769224 + 2.03125 x = 2.106769224 + 2.03125 Combine like terms: 2.106769224 + 2.03125 = 4.138019224 x = 4.138019224 Simplifying x = 4.138019224Subproblem 2
x + -2.03125 = -2.106769224 Simplifying x + -2.03125 = -2.106769224 Reorder the terms: -2.03125 + x = -2.106769224 Solving -2.03125 + x = -2.106769224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.03125' to each side of the equation. -2.03125 + 2.03125 + x = -2.106769224 + 2.03125 Combine like terms: -2.03125 + 2.03125 = 0.00000 0.00000 + x = -2.106769224 + 2.03125 x = -2.106769224 + 2.03125 Combine like terms: -2.106769224 + 2.03125 = -0.075519224 x = -0.075519224 Simplifying x = -0.075519224Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.138019224, -0.075519224}
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