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Simplifying 4x2 + -128x + 901 = 0 Reorder the terms: 901 + -128x + 4x2 = 0 Solving 901 + -128x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 225.25 + -32x + x2 = 0 Move the constant term to the right: Add '-225.25' to each side of the equation. 225.25 + -32x + -225.25 + x2 = 0 + -225.25 Reorder the terms: 225.25 + -225.25 + -32x + x2 = 0 + -225.25 Combine like terms: 225.25 + -225.25 = 0.00 0.00 + -32x + x2 = 0 + -225.25 -32x + x2 = 0 + -225.25 Combine like terms: 0 + -225.25 = -225.25 -32x + x2 = -225.25 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -225.25 + 256 Reorder the terms: 256 + -32x + x2 = -225.25 + 256 Combine like terms: -225.25 + 256 = 30.75 256 + -32x + x2 = 30.75 Factor a perfect square on the left side: (x + -16)(x + -16) = 30.75 Calculate the square root of the right side: 5.545268253 Break this problem into two subproblems by setting (x + -16) equal to 5.545268253 and -5.545268253.Subproblem 1
x + -16 = 5.545268253 Simplifying x + -16 = 5.545268253 Reorder the terms: -16 + x = 5.545268253 Solving -16 + x = 5.545268253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 5.545268253 + 16 Combine like terms: -16 + 16 = 0 0 + x = 5.545268253 + 16 x = 5.545268253 + 16 Combine like terms: 5.545268253 + 16 = 21.545268253 x = 21.545268253 Simplifying x = 21.545268253Subproblem 2
x + -16 = -5.545268253 Simplifying x + -16 = -5.545268253 Reorder the terms: -16 + x = -5.545268253 Solving -16 + x = -5.545268253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -5.545268253 + 16 Combine like terms: -16 + 16 = 0 0 + x = -5.545268253 + 16 x = -5.545268253 + 16 Combine like terms: -5.545268253 + 16 = 10.454731747 x = 10.454731747 Simplifying x = 10.454731747Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.545268253, 10.454731747}
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