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Simplifying 7 + -8x = x2 Solving 7 + -8x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 7 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + 8x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 8x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 8x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8x + x2 = 0 + 7 8x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 8x + x2 = 7 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 7 + 16 Reorder the terms: 16 + 8x + x2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + 8x + x2 = 23 Factor a perfect square on the left side: (x + 4)(x + 4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 4) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 4 = 4.795831523 Simplifying x + 4 = 4.795831523 Reorder the terms: 4 + x = 4.795831523 Solving 4 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.795831523 + -4 x = 4.795831523 + -4 Combine like terms: 4.795831523 + -4 = 0.795831523 x = 0.795831523 Simplifying x = 0.795831523Subproblem 2
x + 4 = -4.795831523 Simplifying x + 4 = -4.795831523 Reorder the terms: 4 + x = -4.795831523 Solving 4 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.795831523 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.795831523 + -4 x = -4.795831523 + -4 Combine like terms: -4.795831523 + -4 = -8.795831523 x = -8.795831523 Simplifying x = -8.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.795831523, -8.795831523}
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