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Simplifying (3x + -9)(3x + -9) = 45 Reorder the terms: (-9 + 3x)(3x + -9) = 45 Reorder the terms: (-9 + 3x)(-9 + 3x) = 45 Multiply (-9 + 3x) * (-9 + 3x) (-9(-9 + 3x) + 3x * (-9 + 3x)) = 45 ((-9 * -9 + 3x * -9) + 3x * (-9 + 3x)) = 45 ((81 + -27x) + 3x * (-9 + 3x)) = 45 (81 + -27x + (-9 * 3x + 3x * 3x)) = 45 (81 + -27x + (-27x + 9x2)) = 45 Combine like terms: -27x + -27x = -54x (81 + -54x + 9x2) = 45 Solving 81 + -54x + 9x2 = 45 Solving for variable 'x'. Reorder the terms: 81 + -45 + -54x + 9x2 = 45 + -45 Combine like terms: 81 + -45 = 36 36 + -54x + 9x2 = 45 + -45 Combine like terms: 45 + -45 = 0 36 + -54x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(4 + -6x + x2) = 0 Ignore the factor 9.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 = 5.236067978 x = 5.236067978 Simplifying x = 5.236067978Subproblem 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 = 0.763932022 x = 0.763932022 Simplifying x = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.236067978, 0.763932022}Solution
x = {5.236067978, 0.763932022}
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