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Simplifying 6x2 + -128x + 64 = 25 Reorder the terms: 64 + -128x + 6x2 = 25 Solving 64 + -128x + 6x2 = 25 Solving for variable 'x'. Reorder the terms: 64 + -25 + -128x + 6x2 = 25 + -25 Combine like terms: 64 + -25 = 39 39 + -128x + 6x2 = 25 + -25 Combine like terms: 25 + -25 = 0 39 + -128x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 6.5 + -21.33333333x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -21.33333333x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -21.33333333x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -21.33333333x + x2 = 0 + -6.5 -21.33333333x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -21.33333333x + x2 = -6.5 The x term is -21.33333333x. Take half its coefficient (-10.66666667). Square it (113.7777778) and add it to both sides. Add '113.7777778' to each side of the equation. -21.33333333x + 113.7777778 + x2 = -6.5 + 113.7777778 Reorder the terms: 113.7777778 + -21.33333333x + x2 = -6.5 + 113.7777778 Combine like terms: -6.5 + 113.7777778 = 107.2777778 113.7777778 + -21.33333333x + x2 = 107.2777778 Factor a perfect square on the left side: (x + -10.66666667)(x + -10.66666667) = 107.2777778 Calculate the square root of the right side: 10.357498627 Break this problem into two subproblems by setting (x + -10.66666667) equal to 10.357498627 and -10.357498627.Subproblem 1
x + -10.66666667 = 10.357498627 Simplifying x + -10.66666667 = 10.357498627 Reorder the terms: -10.66666667 + x = 10.357498627 Solving -10.66666667 + x = 10.357498627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.66666667' to each side of the equation. -10.66666667 + 10.66666667 + x = 10.357498627 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + x = 10.357498627 + 10.66666667 x = 10.357498627 + 10.66666667 Combine like terms: 10.357498627 + 10.66666667 = 21.024165297 x = 21.024165297 Simplifying x = 21.024165297Subproblem 2
x + -10.66666667 = -10.357498627 Simplifying x + -10.66666667 = -10.357498627 Reorder the terms: -10.66666667 + x = -10.357498627 Solving -10.66666667 + x = -10.357498627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.66666667' to each side of the equation. -10.66666667 + 10.66666667 + x = -10.357498627 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + x = -10.357498627 + 10.66666667 x = -10.357498627 + 10.66666667 Combine like terms: -10.357498627 + 10.66666667 = 0.309168043 x = 0.309168043 Simplifying x = 0.309168043Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.024165297, 0.309168043}
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