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Simplifying 4x = x2 + -24 Reorder the terms: 4x = -24 + x2 Solving 4x = -24 + x2 Solving for variable 'x'. Reorder the terms: 24 + 4x + -1x2 = -24 + x2 + 24 + -1x2 Reorder the terms: 24 + 4x + -1x2 = -24 + 24 + x2 + -1x2 Combine like terms: -24 + 24 = 0 24 + 4x + -1x2 = 0 + x2 + -1x2 24 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + -4x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -4x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -4x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -4x + x2 = 0 + 24 -4x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -4x + x2 = 24 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 = 24 + 4 Reorder the terms: 4 + -4x + x2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + -4x + x2 = 28 Factor a perfect square on the left side: (x + -2)(x + -2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -2) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -2 = 5.291502622 Simplifying x + -2 = 5.291502622 Reorder the terms: -2 + x = 5.291502622 Solving -2 + x = 5.291502622 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 = 5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.291502622 + 2 x = 5.291502622 + 2 Combine like terms: 5.291502622 + 2 = 7.291502622 x = 7.291502622 Simplifying x = 7.291502622Subproblem 2
x + -2 = -5.291502622 Simplifying x + -2 = -5.291502622 Reorder the terms: -2 + x = -5.291502622 Solving -2 + x = -5.291502622 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 = -5.291502622 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.291502622 + 2 x = -5.291502622 + 2 Combine like terms: -5.291502622 + 2 = -3.291502622 x = -3.291502622 Simplifying x = -3.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.291502622, -3.291502622}
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