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Simplifying 0 = 2X2 + -4X + -40 Reorder the terms: 0 = -40 + -4X + 2X2 Solving 0 = -40 + -4X + 2X2 Solving for variable 'X'. Combine like terms: 0 + 40 = 40 40 + 4X + -2X2 = -40 + -4X + 2X2 + 40 + 4X + -2X2 Reorder the terms: 40 + 4X + -2X2 = -40 + 40 + -4X + 4X + 2X2 + -2X2 Combine like terms: -40 + 40 = 0 40 + 4X + -2X2 = 0 + -4X + 4X + 2X2 + -2X2 40 + 4X + -2X2 = -4X + 4X + 2X2 + -2X2 Combine like terms: -4X + 4X = 0 40 + 4X + -2X2 = 0 + 2X2 + -2X2 40 + 4X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 40 + 4X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 2X + -1X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 2X + -1X2)' equal to zero and attempt to solve: Simplifying 20 + 2X + -1X2 = 0 Solving 20 + 2X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -2X + X2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2X + 20 + X2 = 0 + 20 Reorder the terms: -20 + 20 + -2X + X2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2X + X2 = 0 + 20 -2X + X2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2X + X2 = 20 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 = 20 + 1 Reorder the terms: 1 + -2X + X2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2X + X2 = 21 Factor a perfect square on the left side: (X + -1)(X + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (X + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
X + -1 = 4.582575695 Simplifying X + -1 = 4.582575695 Reorder the terms: -1 + X = 4.582575695 Solving -1 + X = 4.582575695 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 = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + X = 4.582575695 + 1 X = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 X = 5.582575695 Simplifying X = 5.582575695Subproblem 2
X + -1 = -4.582575695 Simplifying X + -1 = -4.582575695 Reorder the terms: -1 + X = -4.582575695 Solving -1 + X = -4.582575695 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 = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + X = -4.582575695 + 1 X = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 X = -3.582575695 Simplifying X = -3.582575695Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.582575695, -3.582575695}Solution
X = {5.582575695, -3.582575695}
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