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Simplifying -6x2 + 12x + 22 = 0 Reorder the terms: 22 + 12x + -6x2 = 0 Solving 22 + 12x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 6x + -3x2)' equal to zero and attempt to solve: Simplifying 11 + 6x + -3x2 = 0 Solving 11 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3.666666667 + -2x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + -2x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + -2x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + -2x + x2 = 0 + 3.666666667 -2x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 -2x + x2 = 3.666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3.666666667 + 1 Reorder the terms: 1 + -2x + x2 = 3.666666667 + 1 Combine like terms: 3.666666667 + 1 = 4.666666667 1 + -2x + x2 = 4.666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.666666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + -1) equal to 2.1602469 and -2.1602469.Subproblem 1
x + -1 = 2.1602469 Simplifying x + -1 = 2.1602469 Reorder the terms: -1 + x = 2.1602469 Solving -1 + x = 2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.1602469 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.1602469 + 1 x = 2.1602469 + 1 Combine like terms: 2.1602469 + 1 = 3.1602469 x = 3.1602469 Simplifying x = 3.1602469Subproblem 2
x + -1 = -2.1602469 Simplifying x + -1 = -2.1602469 Reorder the terms: -1 + x = -2.1602469 Solving -1 + x = -2.1602469 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.1602469 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.1602469 + 1 x = -2.1602469 + 1 Combine like terms: -2.1602469 + 1 = -1.1602469 x = -1.1602469 Simplifying x = -1.1602469Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1602469, -1.1602469}Solution
x = {3.1602469, -1.1602469}
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