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Simplifying 2x2 + -24x * 71 = 7 Reorder the terms for easier multiplication: 2x2 + -24 * 71x = 7 Multiply -24 * 71 2x2 + -1704x = 7 Reorder the terms: -1704x + 2x2 = 7 Solving -1704x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -1704x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -1704x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -852x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -852x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -852x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -852x + x2 = 0 + 3.5 -852x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -852x + x2 = 3.5 The x term is -852x. Take half its coefficient (-426). Square it (181476) and add it to both sides. Add '181476' to each side of the equation. -852x + 181476 + x2 = 3.5 + 181476 Reorder the terms: 181476 + -852x + x2 = 3.5 + 181476 Combine like terms: 3.5 + 181476 = 181479.5 181476 + -852x + x2 = 181479.5 Factor a perfect square on the left side: (x + -426)(x + -426) = 181479.5 Calculate the square root of the right side: 426.004107961 Break this problem into two subproblems by setting (x + -426) equal to 426.004107961 and -426.004107961.Subproblem 1
x + -426 = 426.004107961 Simplifying x + -426 = 426.004107961 Reorder the terms: -426 + x = 426.004107961 Solving -426 + x = 426.004107961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '426' to each side of the equation. -426 + 426 + x = 426.004107961 + 426 Combine like terms: -426 + 426 = 0 0 + x = 426.004107961 + 426 x = 426.004107961 + 426 Combine like terms: 426.004107961 + 426 = 852.004107961 x = 852.004107961 Simplifying x = 852.004107961Subproblem 2
x + -426 = -426.004107961 Simplifying x + -426 = -426.004107961 Reorder the terms: -426 + x = -426.004107961 Solving -426 + x = -426.004107961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '426' to each side of the equation. -426 + 426 + x = -426.004107961 + 426 Combine like terms: -426 + 426 = 0 0 + x = -426.004107961 + 426 x = -426.004107961 + 426 Combine like terms: -426.004107961 + 426 = -0.004107961 x = -0.004107961 Simplifying x = -0.004107961Solution
The solution to the problem is based on the solutions from the subproblems. x = {852.004107961, -0.004107961}
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