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Simplifying 6x2 + 12x + -4 = 0 Reorder the terms: -4 + 12x + 6x2 = 0 Solving -4 + 12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + 3x2 = 0 Solving -2 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 2x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.6666666667 2x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2x + x2 = 0.6666666667 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 = 0.6666666667 + 1 Reorder the terms: 1 + 2x + x2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + 2x + x2 = 1.6666666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (x + 1) equal to 1.290994449 and -1.290994449.Subproblem 1
x + 1 = 1.290994449 Simplifying x + 1 = 1.290994449 Reorder the terms: 1 + x = 1.290994449 Solving 1 + x = 1.290994449 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 = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.290994449 + -1 x = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 x = 0.290994449 Simplifying x = 0.290994449Subproblem 2
x + 1 = -1.290994449 Simplifying x + 1 = -1.290994449 Reorder the terms: 1 + x = -1.290994449 Solving 1 + x = -1.290994449 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 = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.290994449 + -1 x = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 x = -2.290994449 Simplifying x = -2.290994449Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.290994449, -2.290994449}Solution
x = {0.290994449, -2.290994449}
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