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Simplifying 13(x + 2)(x + 2) + -5 = 22 Reorder the terms: 13(2 + x)(x + 2) + -5 = 22 Reorder the terms: 13(2 + x)(2 + x) + -5 = 22 Multiply (2 + x) * (2 + x) 13(2(2 + x) + x(2 + x)) + -5 = 22 13((2 * 2 + x * 2) + x(2 + x)) + -5 = 22 13((4 + 2x) + x(2 + x)) + -5 = 22 13(4 + 2x + (2 * x + x * x)) + -5 = 22 13(4 + 2x + (2x + x2)) + -5 = 22 Combine like terms: 2x + 2x = 4x 13(4 + 4x + x2) + -5 = 22 (4 * 13 + 4x * 13 + x2 * 13) + -5 = 22 (52 + 52x + 13x2) + -5 = 22 Reorder the terms: 52 + -5 + 52x + 13x2 = 22 Combine like terms: 52 + -5 = 47 47 + 52x + 13x2 = 22 Solving 47 + 52x + 13x2 = 22 Solving for variable 'x'. Reorder the terms: 47 + -22 + 52x + 13x2 = 22 + -22 Combine like terms: 47 + -22 = 25 25 + 52x + 13x2 = 22 + -22 Combine like terms: 22 + -22 = 0 25 + 52x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.923076923 + 4x + x2 = 0 Move the constant term to the right: Add '-1.923076923' to each side of the equation. 1.923076923 + 4x + -1.923076923 + x2 = 0 + -1.923076923 Reorder the terms: 1.923076923 + -1.923076923 + 4x + x2 = 0 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + 4x + x2 = 0 + -1.923076923 4x + x2 = 0 + -1.923076923 Combine like terms: 0 + -1.923076923 = -1.923076923 4x + x2 = -1.923076923 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.923076923 + 4 Reorder the terms: 4 + 4x + x2 = -1.923076923 + 4 Combine like terms: -1.923076923 + 4 = 2.076923077 4 + 4x + x2 = 2.076923077 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.076923077 Calculate the square root of the right side: 1.441153384 Break this problem into two subproblems by setting (x + 2) equal to 1.441153384 and -1.441153384.Subproblem 1
x + 2 = 1.441153384 Simplifying x + 2 = 1.441153384 Reorder the terms: 2 + x = 1.441153384 Solving 2 + x = 1.441153384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.441153384 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.441153384 + -2 x = 1.441153384 + -2 Combine like terms: 1.441153384 + -2 = -0.558846616 x = -0.558846616 Simplifying x = -0.558846616Subproblem 2
x + 2 = -1.441153384 Simplifying x + 2 = -1.441153384 Reorder the terms: 2 + x = -1.441153384 Solving 2 + x = -1.441153384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.441153384 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.441153384 + -2 x = -1.441153384 + -2 Combine like terms: -1.441153384 + -2 = -3.441153384 x = -3.441153384 Simplifying x = -3.441153384Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.558846616, -3.441153384}
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