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Simplifying 90 = x2 + 8x + 56 Reorder the terms: 90 = 56 + 8x + x2 Solving 90 = 56 + 8x + x2 Solving for variable 'x'. Combine like terms: 90 + -56 = 34 34 + -8x + -1x2 = 56 + 8x + x2 + -56 + -8x + -1x2 Reorder the terms: 34 + -8x + -1x2 = 56 + -56 + 8x + -8x + x2 + -1x2 Combine like terms: 56 + -56 = 0 34 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 34 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 34 + -8x + -1x2 = 0 + x2 + -1x2 34 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 34 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -34 + 8x + x2 = 0 Move the constant term to the right: Add '34' to each side of the equation. -34 + 8x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 8x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 8x + x2 = 0 + 34 8x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 8x + x2 = 34 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 = 34 + 16 Reorder the terms: 16 + 8x + x2 = 34 + 16 Combine like terms: 34 + 16 = 50 16 + 8x + x2 = 50 Factor a perfect square on the left side: (x + 4)(x + 4) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 4) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 4 = 7.071067812 Simplifying x + 4 = 7.071067812 Reorder the terms: 4 + x = 7.071067812 Solving 4 + x = 7.071067812 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 = 7.071067812 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.071067812 + -4 x = 7.071067812 + -4 Combine like terms: 7.071067812 + -4 = 3.071067812 x = 3.071067812 Simplifying x = 3.071067812Subproblem 2
x + 4 = -7.071067812 Simplifying x + 4 = -7.071067812 Reorder the terms: 4 + x = -7.071067812 Solving 4 + x = -7.071067812 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 = -7.071067812 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.071067812 + -4 x = -7.071067812 + -4 Combine like terms: -7.071067812 + -4 = -11.071067812 x = -11.071067812 Simplifying x = -11.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.071067812, -11.071067812}
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