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Simplifying 0 = 6x2 + 12x + -16 Reorder the terms: 0 = -16 + 12x + 6x2 Solving 0 = -16 + 12x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 16 = 16 16 + -12x + -6x2 = -16 + 12x + 6x2 + 16 + -12x + -6x2 Reorder the terms: 16 + -12x + -6x2 = -16 + 16 + 12x + -12x + 6x2 + -6x2 Combine like terms: -16 + 16 = 0 16 + -12x + -6x2 = 0 + 12x + -12x + 6x2 + -6x2 16 + -12x + -6x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 16 + -12x + -6x2 = 0 + 6x2 + -6x2 16 + -12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 16 + -12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -6x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -6x + -3x2)' equal to zero and attempt to solve: Simplifying 8 + -6x + -3x2 = 0 Solving 8 + -6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.666666667 + 2x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 2x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 2x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 2x + x2 = 0 + 2.666666667 2x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 2x + x2 = 2.666666667 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 = 2.666666667 + 1 Reorder the terms: 1 + 2x + x2 = 2.666666667 + 1 Combine like terms: 2.666666667 + 1 = 3.666666667 1 + 2x + x2 = 3.666666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + 1) equal to 1.914854216 and -1.914854216.Subproblem 1
x + 1 = 1.914854216 Simplifying x + 1 = 1.914854216 Reorder the terms: 1 + x = 1.914854216 Solving 1 + x = 1.914854216 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 = 1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.914854216 + -1 x = 1.914854216 + -1 Combine like terms: 1.914854216 + -1 = 0.914854216 x = 0.914854216 Simplifying x = 0.914854216Subproblem 2
x + 1 = -1.914854216 Simplifying x + 1 = -1.914854216 Reorder the terms: 1 + x = -1.914854216 Solving 1 + x = -1.914854216 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 = -1.914854216 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.914854216 + -1 x = -1.914854216 + -1 Combine like terms: -1.914854216 + -1 = -2.914854216 x = -2.914854216 Simplifying x = -2.914854216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.914854216, -2.914854216}Solution
x = {0.914854216, -2.914854216}
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