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Simplifying 16x2 + -81x + 100 = 0 Reorder the terms: 100 + -81x + 16x2 = 0 Solving 100 + -81x + 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'. 6.25 + -5.0625x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -5.0625x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -5.0625x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -5.0625x + x2 = 0 + -6.25 -5.0625x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -5.0625x + x2 = -6.25 The x term is -5.0625x. Take half its coefficient (-2.53125). Square it (6.407226563) and add it to both sides. Add '6.407226563' to each side of the equation. -5.0625x + 6.407226563 + x2 = -6.25 + 6.407226563 Reorder the terms: 6.407226563 + -5.0625x + x2 = -6.25 + 6.407226563 Combine like terms: -6.25 + 6.407226563 = 0.157226563 6.407226563 + -5.0625x + x2 = 0.157226563 Factor a perfect square on the left side: (x + -2.53125)(x + -2.53125) = 0.157226563 Calculate the square root of the right side: 0.396518049 Break this problem into two subproblems by setting (x + -2.53125) equal to 0.396518049 and -0.396518049.Subproblem 1
x + -2.53125 = 0.396518049 Simplifying x + -2.53125 = 0.396518049 Reorder the terms: -2.53125 + x = 0.396518049 Solving -2.53125 + x = 0.396518049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.53125' to each side of the equation. -2.53125 + 2.53125 + x = 0.396518049 + 2.53125 Combine like terms: -2.53125 + 2.53125 = 0.00000 0.00000 + x = 0.396518049 + 2.53125 x = 0.396518049 + 2.53125 Combine like terms: 0.396518049 + 2.53125 = 2.927768049 x = 2.927768049 Simplifying x = 2.927768049Subproblem 2
x + -2.53125 = -0.396518049 Simplifying x + -2.53125 = -0.396518049 Reorder the terms: -2.53125 + x = -0.396518049 Solving -2.53125 + x = -0.396518049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.53125' to each side of the equation. -2.53125 + 2.53125 + x = -0.396518049 + 2.53125 Combine like terms: -2.53125 + 2.53125 = 0.00000 0.00000 + x = -0.396518049 + 2.53125 x = -0.396518049 + 2.53125 Combine like terms: -0.396518049 + 2.53125 = 2.134731951 x = 2.134731951 Simplifying x = 2.134731951Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.927768049, 2.134731951}
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