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Simplifying 0 = x2 + -42x + -540 Reorder the terms: 0 = -540 + -42x + x2 Solving 0 = -540 + -42x + x2 Solving for variable 'x'. Combine like terms: 0 + 540 = 540 540 + 42x + -1x2 = -540 + -42x + x2 + 540 + 42x + -1x2 Reorder the terms: 540 + 42x + -1x2 = -540 + 540 + -42x + 42x + x2 + -1x2 Combine like terms: -540 + 540 = 0 540 + 42x + -1x2 = 0 + -42x + 42x + x2 + -1x2 540 + 42x + -1x2 = -42x + 42x + x2 + -1x2 Combine like terms: -42x + 42x = 0 540 + 42x + -1x2 = 0 + x2 + -1x2 540 + 42x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 540 + 42x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -540 + -42x + x2 = 0 Move the constant term to the right: Add '540' to each side of the equation. -540 + -42x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + -42x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + -42x + x2 = 0 + 540 -42x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 -42x + x2 = 540 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = 540 + 441 Reorder the terms: 441 + -42x + x2 = 540 + 441 Combine like terms: 540 + 441 = 981 441 + -42x + x2 = 981 Factor a perfect square on the left side: (x + -21)(x + -21) = 981 Calculate the square root of the right side: 31.320919527 Break this problem into two subproblems by setting (x + -21) equal to 31.320919527 and -31.320919527.Subproblem 1
x + -21 = 31.320919527 Simplifying x + -21 = 31.320919527 Reorder the terms: -21 + x = 31.320919527 Solving -21 + x = 31.320919527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 31.320919527 + 21 Combine like terms: -21 + 21 = 0 0 + x = 31.320919527 + 21 x = 31.320919527 + 21 Combine like terms: 31.320919527 + 21 = 52.320919527 x = 52.320919527 Simplifying x = 52.320919527Subproblem 2
x + -21 = -31.320919527 Simplifying x + -21 = -31.320919527 Reorder the terms: -21 + x = -31.320919527 Solving -21 + x = -31.320919527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -31.320919527 + 21 Combine like terms: -21 + 21 = 0 0 + x = -31.320919527 + 21 x = -31.320919527 + 21 Combine like terms: -31.320919527 + 21 = -10.320919527 x = -10.320919527 Simplifying x = -10.320919527Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.320919527, -10.320919527}
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