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Simplifying 2x * 2x = 412 + -1x Reorder the terms for easier multiplication: 2 * 2x * x = 412 + -1x Multiply 2 * 2 4x * x = 412 + -1x Multiply x * x 4x2 = 412 + -1x Solving 4x2 = 412 + -1x Solving for variable 'x'. Reorder the terms: -412 + x + 4x2 = 412 + -1x + -412 + x Reorder the terms: -412 + x + 4x2 = 412 + -412 + -1x + x Combine like terms: 412 + -412 = 0 -412 + x + 4x2 = 0 + -1x + x -412 + x + 4x2 = -1x + x Combine like terms: -1x + x = 0 -412 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -103 + 0.25x + x2 = 0 Move the constant term to the right: Add '103' to each side of the equation. -103 + 0.25x + 103 + x2 = 0 + 103 Reorder the terms: -103 + 103 + 0.25x + x2 = 0 + 103 Combine like terms: -103 + 103 = 0 0 + 0.25x + x2 = 0 + 103 0.25x + x2 = 0 + 103 Combine like terms: 0 + 103 = 103 0.25x + x2 = 103 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 103 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 103 + 0.25 Combine like terms: 103 + 0.25 = 103.25 0.25 + 0.25x + x2 = 103.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (x + 0.5) equal to 10.161200716 and -10.161200716.Subproblem 1
x + 0.5 = 10.161200716 Simplifying x + 0.5 = 10.161200716 Reorder the terms: 0.5 + x = 10.161200716 Solving 0.5 + x = 10.161200716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.161200716 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.161200716 + -0.5 x = 10.161200716 + -0.5 Combine like terms: 10.161200716 + -0.5 = 9.661200716 x = 9.661200716 Simplifying x = 9.661200716Subproblem 2
x + 0.5 = -10.161200716 Simplifying x + 0.5 = -10.161200716 Reorder the terms: 0.5 + x = -10.161200716 Solving 0.5 + x = -10.161200716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.161200716 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.161200716 + -0.5 x = -10.161200716 + -0.5 Combine like terms: -10.161200716 + -0.5 = -10.661200716 x = -10.661200716 Simplifying x = -10.661200716Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.661200716, -10.661200716}
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