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Simplifying (3 + x)(3 + x) = 160 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) = 160 ((3 * 3 + x * 3) + x(3 + x)) = 160 ((9 + 3x) + x(3 + x)) = 160 (9 + 3x + (3 * x + x * x)) = 160 (9 + 3x + (3x + x2)) = 160 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) = 160 Solving 9 + 6x + x2 = 160 Solving for variable 'x'. Reorder the terms: 9 + -160 + 6x + x2 = 160 + -160 Combine like terms: 9 + -160 = -151 -151 + 6x + x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -151 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '151' to each side of the equation. -151 + 6x + 151 + x2 = 0 + 151 Reorder the terms: -151 + 151 + 6x + x2 = 0 + 151 Combine like terms: -151 + 151 = 0 0 + 6x + x2 = 0 + 151 6x + x2 = 0 + 151 Combine like terms: 0 + 151 = 151 6x + x2 = 151 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 = 151 + 9 Reorder the terms: 9 + 6x + x2 = 151 + 9 Combine like terms: 151 + 9 = 160 9 + 6x + x2 = 160 Factor a perfect square on the left side: (x + 3)(x + 3) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + 3) equal to 12.649110641 and -12.649110641.Subproblem 1
x + 3 = 12.649110641 Simplifying x + 3 = 12.649110641 Reorder the terms: 3 + x = 12.649110641 Solving 3 + x = 12.649110641 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 = 12.649110641 + -3 Combine like terms: 3 + -3 = 0 0 + x = 12.649110641 + -3 x = 12.649110641 + -3 Combine like terms: 12.649110641 + -3 = 9.649110641 x = 9.649110641 Simplifying x = 9.649110641Subproblem 2
x + 3 = -12.649110641 Simplifying x + 3 = -12.649110641 Reorder the terms: 3 + x = -12.649110641 Solving 3 + x = -12.649110641 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 = -12.649110641 + -3 Combine like terms: 3 + -3 = 0 0 + x = -12.649110641 + -3 x = -12.649110641 + -3 Combine like terms: -12.649110641 + -3 = -15.649110641 x = -15.649110641 Simplifying x = -15.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.649110641, -15.649110641}
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