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Simplifying 5 = (x + 3)(x + 3) Reorder the terms: 5 = (3 + x)(x + 3) Reorder the terms: 5 = (3 + x)(3 + x) Multiply (3 + x) * (3 + x) 5 = (3(3 + x) + x(3 + x)) 5 = ((3 * 3 + x * 3) + x(3 + x)) 5 = ((9 + 3x) + x(3 + x)) 5 = (9 + 3x + (3 * x + x * x)) 5 = (9 + 3x + (3x + x2)) Combine like terms: 3x + 3x = 6x 5 = (9 + 6x + x2) Solving 5 = 9 + 6x + x2 Solving for variable 'x'. Combine like terms: 5 + -9 = -4 -4 + -6x + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2 Reorder the terms: -4 + -6x + -1x2 = 9 + -9 + 6x + -6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -4 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -4 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -4 + -6x + -1x2 = 0 + x2 + -1x2 -4 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 6x + x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + x2 = 0 Solving 4 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 6x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6x + x2 = 0 + -4 6x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 6x + x2 = -4 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 = -4 + 9 Reorder the terms: 9 + 6x + x2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6x + x2 = 5 Factor a perfect square on the left side: (x + 3)(x + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 3 = 2.236067978 Simplifying x + 3 = 2.236067978 Reorder the terms: 3 + x = 2.236067978 Solving 3 + x = 2.236067978 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 = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.236067978 + -3 x = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 x = -0.763932022 Simplifying x = -0.763932022Subproblem 2
x + 3 = -2.236067978 Simplifying x + 3 = -2.236067978 Reorder the terms: 3 + x = -2.236067978 Solving 3 + x = -2.236067978 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 = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.236067978 + -3 x = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 x = -5.236067978 Simplifying x = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.763932022, -5.236067978}Solution
x = {-0.763932022, -5.236067978}
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