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Simplifying 6x2 + -12x + -21 = 0 Reorder the terms: -21 + -12x + 6x2 = 0 Solving -21 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -4x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + -4x + 2x2 = 0 Solving -7 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -2x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2x + x2 = 0 + 3.5 -2x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2x + x2 = 3.5 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 = 3.5 + 1 Reorder the terms: 1 + -2x + x2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + -2x + x2 = 4.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -1) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -1 = 2.121320344 Simplifying x + -1 = 2.121320344 Reorder the terms: -1 + x = 2.121320344 Solving -1 + x = 2.121320344 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 = 2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.121320344 + 1 x = 2.121320344 + 1 Combine like terms: 2.121320344 + 1 = 3.121320344 x = 3.121320344 Simplifying x = 3.121320344Subproblem 2
x + -1 = -2.121320344 Simplifying x + -1 = -2.121320344 Reorder the terms: -1 + x = -2.121320344 Solving -1 + x = -2.121320344 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 = -2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.121320344 + 1 x = -2.121320344 + 1 Combine like terms: -2.121320344 + 1 = -1.121320344 x = -1.121320344 Simplifying x = -1.121320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.121320344, -1.121320344}Solution
x = {3.121320344, -1.121320344}
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