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Simplifying x2 + -2x + 4 = 8x + -4 Reorder the terms: 4 + -2x + x2 = 8x + -4 Reorder the terms: 4 + -2x + x2 = -4 + 8x Solving 4 + -2x + x2 = -4 + 8x Solving for variable 'x'. Reorder the terms: 4 + 4 + -2x + -8x + x2 = -4 + 8x + 4 + -8x Combine like terms: 4 + 4 = 8 8 + -2x + -8x + x2 = -4 + 8x + 4 + -8x Combine like terms: -2x + -8x = -10x 8 + -10x + x2 = -4 + 8x + 4 + -8x Reorder the terms: 8 + -10x + x2 = -4 + 4 + 8x + -8x Combine like terms: -4 + 4 = 0 8 + -10x + x2 = 0 + 8x + -8x 8 + -10x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 8 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -10x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -10x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -10x + x2 = 0 + -8 -10x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -10x + x2 = -8 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -8 + 25 Reorder the terms: 25 + -10x + x2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + -10x + x2 = 17 Factor a perfect square on the left side: (x + -5)(x + -5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -5) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -5 = 4.123105626 Simplifying x + -5 = 4.123105626 Reorder the terms: -5 + x = 4.123105626 Solving -5 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.123105626 + 5 x = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 x = 9.123105626 Simplifying x = 9.123105626Subproblem 2
x + -5 = -4.123105626 Simplifying x + -5 = -4.123105626 Reorder the terms: -5 + x = -4.123105626 Solving -5 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.123105626 + 5 x = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 x = 0.876894374 Simplifying x = 0.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.123105626, 0.876894374}
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