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Simplifying 8 + -1x2 = 12 + 6x Solving 8 + -1x2 = 12 + 6x Solving for variable 'x'. Reorder the terms: 8 + -12 + -6x + -1x2 = 12 + 6x + -12 + -6x Combine like terms: 8 + -12 = -4 -4 + -6x + -1x2 = 12 + 6x + -12 + -6x Reorder the terms: -4 + -6x + -1x2 = 12 + -12 + 6x + -6x Combine like terms: 12 + -12 = 0 -4 + -6x + -1x2 = 0 + 6x + -6x -4 + -6x + -1x2 = 6x + -6x Combine like terms: 6x + -6x = 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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