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Simplifying 0 = 2x2 + -20x + 4 Reorder the terms: 0 = 4 + -20x + 2x2 Solving 0 = 4 + -20x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + 20x + -2x2 = 4 + -20x + 2x2 + -4 + 20x + -2x2 Reorder the terms: -4 + 20x + -2x2 = 4 + -4 + -20x + 20x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 -4 + 20x + -2x2 = 0 + -20x + 20x + 2x2 + -2x2 -4 + 20x + -2x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 -4 + 20x + -2x2 = 0 + 2x2 + -2x2 -4 + 20x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + 20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 10x + -1x2 = 0 Solving -2 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -10x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -10x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -10x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -10x + x2 = 0 + -2 -10x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -10x + x2 = -2 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 = -2 + 25 Reorder the terms: 25 + -10x + x2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + -10x + x2 = 23 Factor a perfect square on the left side: (x + -5)(x + -5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -5) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -5 = 4.795831523 Simplifying x + -5 = 4.795831523 Reorder the terms: -5 + x = 4.795831523 Solving -5 + x = 4.795831523 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 = 4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.795831523 + 5 x = 4.795831523 + 5 Combine like terms: 4.795831523 + 5 = 9.795831523 x = 9.795831523 Simplifying x = 9.795831523Subproblem 2
x + -5 = -4.795831523 Simplifying x + -5 = -4.795831523 Reorder the terms: -5 + x = -4.795831523 Solving -5 + x = -4.795831523 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 = -4.795831523 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.795831523 + 5 x = -4.795831523 + 5 Combine like terms: -4.795831523 + 5 = 0.204168477 x = 0.204168477 Simplifying x = 0.204168477Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.795831523, 0.204168477}Solution
x = {9.795831523, 0.204168477}
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