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Simplifying -2X2 + -8X = -2 Reorder the terms: -8X + -2X2 = -2 Solving -8X + -2X2 = -2 Solving for variable 'X'. Reorder the terms: 2 + -8X + -2X2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -8X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -4X + -1X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4X + -1X2)' equal to zero and attempt to solve: Simplifying 1 + -4X + -1X2 = 0 Solving 1 + -4X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 4X + X2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 4X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4X + X2 = 0 + 1 4X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 4X + X2 = 1 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 1 + 4 Reorder the terms: 4 + 4X + X2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4X + X2 = 5 Factor a perfect square on the left side: (X + 2)(X + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (X + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
X + 2 = 2.236067978 Simplifying X + 2 = 2.236067978 Reorder the terms: 2 + X = 2.236067978 Solving 2 + X = 2.236067978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + X = 2.236067978 + -2 X = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 X = 0.236067978 Simplifying X = 0.236067978Subproblem 2
X + 2 = -2.236067978 Simplifying X + 2 = -2.236067978 Reorder the terms: 2 + X = -2.236067978 Solving 2 + X = -2.236067978 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + X = -2.236067978 + -2 X = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 X = -4.236067978 Simplifying X = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.236067978, -4.236067978}Solution
X = {0.236067978, -4.236067978}
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