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Simplifying -2x + 24 = x2 + 4x + -32 Reorder the terms: 24 + -2x = x2 + 4x + -32 Reorder the terms: 24 + -2x = -32 + 4x + x2 Solving 24 + -2x = -32 + 4x + x2 Solving for variable 'x'. Reorder the terms: 24 + 32 + -2x + -4x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2 Combine like terms: 24 + 32 = 56 56 + -2x + -4x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2 Combine like terms: -2x + -4x = -6x 56 + -6x + -1x2 = -32 + 4x + x2 + 32 + -4x + -1x2 Reorder the terms: 56 + -6x + -1x2 = -32 + 32 + 4x + -4x + x2 + -1x2 Combine like terms: -32 + 32 = 0 56 + -6x + -1x2 = 0 + 4x + -4x + x2 + -1x2 56 + -6x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 56 + -6x + -1x2 = 0 + x2 + -1x2 56 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 56 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -56 + 6x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 6x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 6x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 6x + x2 = 0 + 56 6x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 6x + x2 = 56 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 56 + 9 Reorder the terms: 9 + 6x + x2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + 6x + x2 = 65 Factor a perfect square on the left side: (x + 3)(x + 3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 3) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 3 = 8.062257748 Simplifying x + 3 = 8.062257748 Reorder the terms: 3 + x = 8.062257748 Solving 3 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.062257748 + -3 x = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 x = 5.062257748 Simplifying x = 5.062257748Subproblem 2
x + 3 = -8.062257748 Simplifying x + 3 = -8.062257748 Reorder the terms: 3 + x = -8.062257748 Solving 3 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.062257748 + -3 x = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 x = -11.062257748 Simplifying x = -11.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.062257748, -11.062257748}
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