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Simplifying 4x2 + 6 = 300 + -3x Reorder the terms: 6 + 4x2 = 300 + -3x Solving 6 + 4x2 = 300 + -3x Solving for variable 'x'. Reorder the terms: 6 + -300 + 3x + 4x2 = 300 + -3x + -300 + 3x Combine like terms: 6 + -300 = -294 -294 + 3x + 4x2 = 300 + -3x + -300 + 3x Reorder the terms: -294 + 3x + 4x2 = 300 + -300 + -3x + 3x Combine like terms: 300 + -300 = 0 -294 + 3x + 4x2 = 0 + -3x + 3x -294 + 3x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -294 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -73.5 + 0.75x + x2 = 0 Move the constant term to the right: Add '73.5' to each side of the equation. -73.5 + 0.75x + 73.5 + x2 = 0 + 73.5 Reorder the terms: -73.5 + 73.5 + 0.75x + x2 = 0 + 73.5 Combine like terms: -73.5 + 73.5 = 0.0 0.0 + 0.75x + x2 = 0 + 73.5 0.75x + x2 = 0 + 73.5 Combine like terms: 0 + 73.5 = 73.5 0.75x + x2 = 73.5 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 73.5 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 73.5 + 0.140625 Combine like terms: 73.5 + 0.140625 = 73.640625 0.140625 + 0.75x + x2 = 73.640625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 73.640625 Calculate the square root of the right side: 8.581411597 Break this problem into two subproblems by setting (x + 0.375) equal to 8.581411597 and -8.581411597.Subproblem 1
x + 0.375 = 8.581411597 Simplifying x + 0.375 = 8.581411597 Reorder the terms: 0.375 + x = 8.581411597 Solving 0.375 + x = 8.581411597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 8.581411597 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 8.581411597 + -0.375 x = 8.581411597 + -0.375 Combine like terms: 8.581411597 + -0.375 = 8.206411597 x = 8.206411597 Simplifying x = 8.206411597Subproblem 2
x + 0.375 = -8.581411597 Simplifying x + 0.375 = -8.581411597 Reorder the terms: 0.375 + x = -8.581411597 Solving 0.375 + x = -8.581411597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -8.581411597 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -8.581411597 + -0.375 x = -8.581411597 + -0.375 Combine like terms: -8.581411597 + -0.375 = -8.956411597 x = -8.956411597 Simplifying x = -8.956411597Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.206411597, -8.956411597}
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