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Simplifying 50 = (x + 3)(x + 3) Reorder the terms: 50 = (3 + x)(x + 3) Reorder the terms: 50 = (3 + x)(3 + x) Multiply (3 + x) * (3 + x) 50 = (3(3 + x) + x(3 + x)) 50 = ((3 * 3 + x * 3) + x(3 + x)) 50 = ((9 + 3x) + x(3 + x)) 50 = (9 + 3x + (3 * x + x * x)) 50 = (9 + 3x + (3x + x2)) Combine like terms: 3x + 3x = 6x 50 = (9 + 6x + x2) Solving 50 = 9 + 6x + x2 Solving for variable 'x'. Combine like terms: 50 + -9 = 41 41 + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: 41 + -6x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 41 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 41 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 41 + -6x + -1x2 = 0 + x2 + -1x2 41 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 41 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + 6x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 6x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 6x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 6x + x2 = 0 + 41 6x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 6x + x2 = 41 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 = 41 + 9 Reorder the terms: 9 + 6x + x2 = 41 + 9 Combine like terms: 41 + 9 = 50 9 + 6x + x2 = 50 Factor a perfect square on the left side: (x + 3)(x + 3) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 3) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 3 = 7.071067812 Simplifying x + 3 = 7.071067812 Reorder the terms: 3 + x = 7.071067812 Solving 3 + x = 7.071067812 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 = 7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.071067812 + -3 x = 7.071067812 + -3 Combine like terms: 7.071067812 + -3 = 4.071067812 x = 4.071067812 Simplifying x = 4.071067812Subproblem 2
x + 3 = -7.071067812 Simplifying x + 3 = -7.071067812 Reorder the terms: 3 + x = -7.071067812 Solving 3 + x = -7.071067812 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 = -7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.071067812 + -3 x = -7.071067812 + -3 Combine like terms: -7.071067812 + -3 = -10.071067812 x = -10.071067812 Simplifying x = -10.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.071067812, -10.071067812}
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