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Simplifying 3x + 8 = 64x2 + -80x + 25 Reorder the terms: 8 + 3x = 64x2 + -80x + 25 Reorder the terms: 8 + 3x = 25 + -80x + 64x2 Solving 8 + 3x = 25 + -80x + 64x2 Solving for variable 'x'. Reorder the terms: 8 + -25 + 3x + 80x + -64x2 = 25 + -80x + 64x2 + -25 + 80x + -64x2 Combine like terms: 8 + -25 = -17 -17 + 3x + 80x + -64x2 = 25 + -80x + 64x2 + -25 + 80x + -64x2 Combine like terms: 3x + 80x = 83x -17 + 83x + -64x2 = 25 + -80x + 64x2 + -25 + 80x + -64x2 Reorder the terms: -17 + 83x + -64x2 = 25 + -25 + -80x + 80x + 64x2 + -64x2 Combine like terms: 25 + -25 = 0 -17 + 83x + -64x2 = 0 + -80x + 80x + 64x2 + -64x2 -17 + 83x + -64x2 = -80x + 80x + 64x2 + -64x2 Combine like terms: -80x + 80x = 0 -17 + 83x + -64x2 = 0 + 64x2 + -64x2 -17 + 83x + -64x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 -17 + 83x + -64x2 = 0 Begin completing the square. Divide all terms by -64 the coefficient of the squared term: Divide each side by '-64'. 0.265625 + -1.296875x + x2 = 0 Move the constant term to the right: Add '-0.265625' to each side of the equation. 0.265625 + -1.296875x + -0.265625 + x2 = 0 + -0.265625 Reorder the terms: 0.265625 + -0.265625 + -1.296875x + x2 = 0 + -0.265625 Combine like terms: 0.265625 + -0.265625 = 0.000000 0.000000 + -1.296875x + x2 = 0 + -0.265625 -1.296875x + x2 = 0 + -0.265625 Combine like terms: 0 + -0.265625 = -0.265625 -1.296875x + x2 = -0.265625 The x term is -1.296875x. Take half its coefficient (-0.6484375). Square it (0.4204711914) and add it to both sides. Add '0.4204711914' to each side of the equation. -1.296875x + 0.4204711914 + x2 = -0.265625 + 0.4204711914 Reorder the terms: 0.4204711914 + -1.296875x + x2 = -0.265625 + 0.4204711914 Combine like terms: -0.265625 + 0.4204711914 = 0.1548461914 0.4204711914 + -1.296875x + x2 = 0.1548461914 Factor a perfect square on the left side: (x + -0.6484375)(x + -0.6484375) = 0.1548461914 Calculate the square root of the right side: 0.393505008 Break this problem into two subproblems by setting (x + -0.6484375) equal to 0.393505008 and -0.393505008.Subproblem 1
x + -0.6484375 = 0.393505008 Simplifying x + -0.6484375 = 0.393505008 Reorder the terms: -0.6484375 + x = 0.393505008 Solving -0.6484375 + x = 0.393505008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6484375' to each side of the equation. -0.6484375 + 0.6484375 + x = 0.393505008 + 0.6484375 Combine like terms: -0.6484375 + 0.6484375 = 0.0000000 0.0000000 + x = 0.393505008 + 0.6484375 x = 0.393505008 + 0.6484375 Combine like terms: 0.393505008 + 0.6484375 = 1.041942508 x = 1.041942508 Simplifying x = 1.041942508Subproblem 2
x + -0.6484375 = -0.393505008 Simplifying x + -0.6484375 = -0.393505008 Reorder the terms: -0.6484375 + x = -0.393505008 Solving -0.6484375 + x = -0.393505008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6484375' to each side of the equation. -0.6484375 + 0.6484375 + x = -0.393505008 + 0.6484375 Combine like terms: -0.6484375 + 0.6484375 = 0.0000000 0.0000000 + x = -0.393505008 + 0.6484375 x = -0.393505008 + 0.6484375 Combine like terms: -0.393505008 + 0.6484375 = 0.254932492 x = 0.254932492 Simplifying x = 0.254932492Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041942508, 0.254932492}
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