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Simplifying 2x2 + -20x + -12 = 0 Reorder the terms: -12 + -20x + 2x2 = 0 Solving -12 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -10x + x2)' equal to zero and attempt to solve: Simplifying -6 + -10x + x2 = 0 Solving -6 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -10x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -10x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -10x + x2 = 0 + 6 -10x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -10x + x2 = 6 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 6 + 25 Reorder the terms: 25 + -10x + x2 = 6 + 25 Combine like terms: 6 + 25 = 31 25 + -10x + x2 = 31 Factor a perfect square on the left side: (x + -5)(x + -5) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -5) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -5 = 5.567764363 Simplifying x + -5 = 5.567764363 Reorder the terms: -5 + x = 5.567764363 Solving -5 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.567764363 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.567764363 + 5 x = 5.567764363 + 5 Combine like terms: 5.567764363 + 5 = 10.567764363 x = 10.567764363 Simplifying x = 10.567764363Subproblem 2
x + -5 = -5.567764363 Simplifying x + -5 = -5.567764363 Reorder the terms: -5 + x = -5.567764363 Solving -5 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.567764363 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.567764363 + 5 x = -5.567764363 + 5 Combine like terms: -5.567764363 + 5 = -0.567764363 x = -0.567764363 Simplifying x = -0.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.567764363, -0.567764363}Solution
x = {10.567764363, -0.567764363}
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