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Simplifying 4x * 4x = 8x + 5 Reorder the terms for easier multiplication: 4 * 4x * x = 8x + 5 Multiply 4 * 4 16x * x = 8x + 5 Multiply x * x 16x2 = 8x + 5 Reorder the terms: 16x2 = 5 + 8x Solving 16x2 = 5 + 8x Solving for variable 'x'. Reorder the terms: -5 + -8x + 16x2 = 5 + 8x + -5 + -8x Reorder the terms: -5 + -8x + 16x2 = 5 + -5 + 8x + -8x Combine like terms: 5 + -5 = 0 -5 + -8x + 16x2 = 0 + 8x + -8x -5 + -8x + 16x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -5 + -8x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.5x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.5x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.5x + x2 = 0 + 0.3125 -0.5x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.5x + x2 = 0.3125 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.3125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.3125 + 0.0625 Combine like terms: 0.3125 + 0.0625 = 0.375 0.0625 + -0.5x + x2 = 0.375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + -0.25) equal to 0.612372436 and -0.612372436.Subproblem 1
x + -0.25 = 0.612372436 Simplifying x + -0.25 = 0.612372436 Reorder the terms: -0.25 + x = 0.612372436 Solving -0.25 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.612372436 + 0.25 x = 0.612372436 + 0.25 Combine like terms: 0.612372436 + 0.25 = 0.862372436 x = 0.862372436 Simplifying x = 0.862372436Subproblem 2
x + -0.25 = -0.612372436 Simplifying x + -0.25 = -0.612372436 Reorder the terms: -0.25 + x = -0.612372436 Solving -0.25 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.612372436 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.612372436 + 0.25 x = -0.612372436 + 0.25 Combine like terms: -0.612372436 + 0.25 = -0.362372436 x = -0.362372436 Simplifying x = -0.362372436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.862372436, -0.362372436}
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