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Simplifying 540 = 4x2 + 23x Reorder the terms: 540 = 23x + 4x2 Solving 540 = 23x + 4x2 Solving for variable 'x'. Reorder the terms: 540 + -23x + -4x2 = 23x + -23x + 4x2 + -4x2 Combine like terms: 23x + -23x = 0 540 + -23x + -4x2 = 0 + 4x2 + -4x2 540 + -23x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 540 + -23x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -135 + 5.75x + x2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + 5.75x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 5.75x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 5.75x + x2 = 0 + 135 5.75x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 5.75x + x2 = 135 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 135 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 135 + 8.265625 Combine like terms: 135 + 8.265625 = 143.265625 8.265625 + 5.75x + x2 = 143.265625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 143.265625 Calculate the square root of the right side: 11.96936193 Break this problem into two subproblems by setting (x + 2.875) equal to 11.96936193 and -11.96936193.Subproblem 1
x + 2.875 = 11.96936193 Simplifying x + 2.875 = 11.96936193 Reorder the terms: 2.875 + x = 11.96936193 Solving 2.875 + x = 11.96936193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 11.96936193 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 11.96936193 + -2.875 x = 11.96936193 + -2.875 Combine like terms: 11.96936193 + -2.875 = 9.09436193 x = 9.09436193 Simplifying x = 9.09436193Subproblem 2
x + 2.875 = -11.96936193 Simplifying x + 2.875 = -11.96936193 Reorder the terms: 2.875 + x = -11.96936193 Solving 2.875 + x = -11.96936193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -11.96936193 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -11.96936193 + -2.875 x = -11.96936193 + -2.875 Combine like terms: -11.96936193 + -2.875 = -14.84436193 x = -14.84436193 Simplifying x = -14.84436193Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.09436193, -14.84436193}
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