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Simplifying 28 = (x + 3)(x + 3) Reorder the terms: 28 = (3 + x)(x + 3) Reorder the terms: 28 = (3 + x)(3 + x) Multiply (3 + x) * (3 + x) 28 = (3(3 + x) + x(3 + x)) 28 = ((3 * 3 + x * 3) + x(3 + x)) 28 = ((9 + 3x) + x(3 + x)) 28 = (9 + 3x + (3 * x + x * x)) 28 = (9 + 3x + (3x + x2)) Combine like terms: 3x + 3x = 6x 28 = (9 + 6x + x2) Solving 28 = 9 + 6x + x2 Solving for variable 'x'. Combine like terms: 28 + -9 = 19 19 + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: 19 + -6x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 19 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 19 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 19 + -6x + -1x2 = 0 + x2 + -1x2 19 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 6x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6x + x2 = 0 + 19 6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 6x + x2 = 19 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 = 19 + 9 Reorder the terms: 9 + 6x + x2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + 6x + x2 = 28 Factor a perfect square on the left side: (x + 3)(x + 3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 3) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 3 = 5.291502622 Simplifying x + 3 = 5.291502622 Reorder the terms: 3 + x = 5.291502622 Solving 3 + x = 5.291502622 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 = 5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.291502622 + -3 x = 5.291502622 + -3 Combine like terms: 5.291502622 + -3 = 2.291502622 x = 2.291502622 Simplifying x = 2.291502622Subproblem 2
x + 3 = -5.291502622 Simplifying x + 3 = -5.291502622 Reorder the terms: 3 + x = -5.291502622 Solving 3 + x = -5.291502622 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 = -5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.291502622 + -3 x = -5.291502622 + -3 Combine like terms: -5.291502622 + -3 = -8.291502622 x = -8.291502622 Simplifying x = -8.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.291502622, -8.291502622}
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