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Simplifying x * 4x = 8 * 12 + x Reorder the terms for easier multiplication: 4x * x = 8 * 12 + x Multiply x * x 4x2 = 8 * 12 + x Multiply 8 * 12 4x2 = 96 + x Solving 4x2 = 96 + x Solving for variable 'x'. Reorder the terms: -96 + -1x + 4x2 = 96 + x + -96 + -1x Reorder the terms: -96 + -1x + 4x2 = 96 + -96 + x + -1x Combine like terms: 96 + -96 = 0 -96 + -1x + 4x2 = 0 + x + -1x -96 + -1x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -96 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -24 + -0.25x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -0.25x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -0.25x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -0.25x + x2 = 0 + 24 -0.25x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -0.25x + x2 = 24 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 24 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 24 + 0.015625 Combine like terms: 24 + 0.015625 = 24.015625 0.015625 + -0.25x + x2 = 24.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 24.015625 Calculate the square root of the right side: 4.900573946 Break this problem into two subproblems by setting (x + -0.125) equal to 4.900573946 and -4.900573946.Subproblem 1
x + -0.125 = 4.900573946 Simplifying x + -0.125 = 4.900573946 Reorder the terms: -0.125 + x = 4.900573946 Solving -0.125 + x = 4.900573946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 4.900573946 + 0.125 x = 4.900573946 + 0.125 Combine like terms: 4.900573946 + 0.125 = 5.025573946 x = 5.025573946 Simplifying x = 5.025573946Subproblem 2
x + -0.125 = -4.900573946 Simplifying x + -0.125 = -4.900573946 Reorder the terms: -0.125 + x = -4.900573946 Solving -0.125 + x = -4.900573946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -4.900573946 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -4.900573946 + 0.125 x = -4.900573946 + 0.125 Combine like terms: -4.900573946 + 0.125 = -4.775573946 x = -4.775573946 Simplifying x = -4.775573946Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.025573946, -4.775573946}
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