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Simplifying 6 = 2(x + -3)(x + -3) + -1 Reorder the terms: 6 = 2(-3 + x)(x + -3) + -1 Reorder the terms: 6 = 2(-3 + x)(-3 + x) + -1 Multiply (-3 + x) * (-3 + x) 6 = 2(-3(-3 + x) + x(-3 + x)) + -1 6 = 2((-3 * -3 + x * -3) + x(-3 + x)) + -1 6 = 2((9 + -3x) + x(-3 + x)) + -1 6 = 2(9 + -3x + (-3 * x + x * x)) + -1 6 = 2(9 + -3x + (-3x + x2)) + -1 Combine like terms: -3x + -3x = -6x 6 = 2(9 + -6x + x2) + -1 6 = (9 * 2 + -6x * 2 + x2 * 2) + -1 6 = (18 + -12x + 2x2) + -1 Reorder the terms: 6 = 18 + -1 + -12x + 2x2 Combine like terms: 18 + -1 = 17 6 = 17 + -12x + 2x2 Solving 6 = 17 + -12x + 2x2 Solving for variable 'x'. Combine like terms: 6 + -17 = -11 -11 + 12x + -2x2 = 17 + -12x + 2x2 + -17 + 12x + -2x2 Reorder the terms: -11 + 12x + -2x2 = 17 + -17 + -12x + 12x + 2x2 + -2x2 Combine like terms: 17 + -17 = 0 -11 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2 -11 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 -11 + 12x + -2x2 = 0 + 2x2 + -2x2 -11 + 12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -11 + 12x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5.5 + -6x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -6x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -6x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -6x + x2 = 0 + -5.5 -6x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -6x + x2 = -5.5 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 = -5.5 + 9 Reorder the terms: 9 + -6x + x2 = -5.5 + 9 Combine like terms: -5.5 + 9 = 3.5 9 + -6x + x2 = 3.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -3) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -3 = 1.870828693 Simplifying x + -3 = 1.870828693 Reorder the terms: -3 + x = 1.870828693 Solving -3 + x = 1.870828693 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 = 1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.870828693 + 3 x = 1.870828693 + 3 Combine like terms: 1.870828693 + 3 = 4.870828693 x = 4.870828693 Simplifying x = 4.870828693Subproblem 2
x + -3 = -1.870828693 Simplifying x + -3 = -1.870828693 Reorder the terms: -3 + x = -1.870828693 Solving -3 + x = -1.870828693 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 = -1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.870828693 + 3 x = -1.870828693 + 3 Combine like terms: -1.870828693 + 3 = 1.129171307 x = 1.129171307 Simplifying x = 1.129171307Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.870828693, 1.129171307}
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