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Simplifying 0 = x2 + 4x + -540 Reorder the terms: 0 = -540 + 4x + x2 Solving 0 = -540 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + 540 = 540 540 + -4x + -1x2 = -540 + 4x + x2 + 540 + -4x + -1x2 Reorder the terms: 540 + -4x + -1x2 = -540 + 540 + 4x + -4x + x2 + -1x2 Combine like terms: -540 + 540 = 0 540 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 540 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 540 + -4x + -1x2 = 0 + x2 + -1x2 540 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 540 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -540 + 4x + x2 = 0 Move the constant term to the right: Add '540' to each side of the equation. -540 + 4x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 4x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 4x + x2 = 0 + 540 4x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 4x + x2 = 540 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 540 + 4 Reorder the terms: 4 + 4x + x2 = 540 + 4 Combine like terms: 540 + 4 = 544 4 + 4x + x2 = 544 Factor a perfect square on the left side: (x + 2)(x + 2) = 544 Calculate the square root of the right side: 23.323807579 Break this problem into two subproblems by setting (x + 2) equal to 23.323807579 and -23.323807579.Subproblem 1
x + 2 = 23.323807579 Simplifying x + 2 = 23.323807579 Reorder the terms: 2 + x = 23.323807579 Solving 2 + x = 23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 23.323807579 + -2 Combine like terms: 2 + -2 = 0 0 + x = 23.323807579 + -2 x = 23.323807579 + -2 Combine like terms: 23.323807579 + -2 = 21.323807579 x = 21.323807579 Simplifying x = 21.323807579Subproblem 2
x + 2 = -23.323807579 Simplifying x + 2 = -23.323807579 Reorder the terms: 2 + x = -23.323807579 Solving 2 + x = -23.323807579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -23.323807579 + -2 Combine like terms: 2 + -2 = 0 0 + x = -23.323807579 + -2 x = -23.323807579 + -2 Combine like terms: -23.323807579 + -2 = -25.323807579 x = -25.323807579 Simplifying x = -25.323807579Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.323807579, -25.323807579}
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