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Simplifying -16x2 + 25x + 8 = 0 Reorder the terms: 8 + 25x + -16x2 = 0 Solving 8 + 25x + -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'. -0.5 + -1.5625x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.5625x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.5625x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.5625x + x2 = 0 + 0.5 -1.5625x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.5625x + x2 = 0.5 The x term is -1.5625x. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625x + 0.6103515625 + x2 = 0.5 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625x + x2 = 0.5 + 0.6103515625 Combine like terms: 0.5 + 0.6103515625 = 1.1103515625 0.6103515625 + -1.5625x + x2 = 1.1103515625 Factor a perfect square on the left side: (x + -0.78125)(x + -0.78125) = 1.1103515625 Calculate the square root of the right side: 1.053732206 Break this problem into two subproblems by setting (x + -0.78125) equal to 1.053732206 and -1.053732206.Subproblem 1
x + -0.78125 = 1.053732206 Simplifying x + -0.78125 = 1.053732206 Reorder the terms: -0.78125 + x = 1.053732206 Solving -0.78125 + x = 1.053732206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = 1.053732206 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = 1.053732206 + 0.78125 x = 1.053732206 + 0.78125 Combine like terms: 1.053732206 + 0.78125 = 1.834982206 x = 1.834982206 Simplifying x = 1.834982206Subproblem 2
x + -0.78125 = -1.053732206 Simplifying x + -0.78125 = -1.053732206 Reorder the terms: -0.78125 + x = -1.053732206 Solving -0.78125 + x = -1.053732206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = -1.053732206 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = -1.053732206 + 0.78125 x = -1.053732206 + 0.78125 Combine like terms: -1.053732206 + 0.78125 = -0.272482206 x = -0.272482206 Simplifying x = -0.272482206Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.834982206, -0.272482206}
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