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Simplifying 100 + 400x + -5x2 = 0 Solving 100 + 400x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 80x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + 80x + -1x2)' equal to zero and attempt to solve: Simplifying 20 + 80x + -1x2 = 0 Solving 20 + 80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -80x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -80x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -80x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -80x + x2 = 0 + 20 -80x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -80x + x2 = 20 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = 20 + 1600 Reorder the terms: 1600 + -80x + x2 = 20 + 1600 Combine like terms: 20 + 1600 = 1620 1600 + -80x + x2 = 1620 Factor a perfect square on the left side: (x + -40)(x + -40) = 1620 Calculate the square root of the right side: 40.249223595 Break this problem into two subproblems by setting (x + -40) equal to 40.249223595 and -40.249223595.Subproblem 1
x + -40 = 40.249223595 Simplifying x + -40 = 40.249223595 Reorder the terms: -40 + x = 40.249223595 Solving -40 + x = 40.249223595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 40.249223595 + 40 Combine like terms: -40 + 40 = 0 0 + x = 40.249223595 + 40 x = 40.249223595 + 40 Combine like terms: 40.249223595 + 40 = 80.249223595 x = 80.249223595 Simplifying x = 80.249223595Subproblem 2
x + -40 = -40.249223595 Simplifying x + -40 = -40.249223595 Reorder the terms: -40 + x = -40.249223595 Solving -40 + x = -40.249223595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -40.249223595 + 40 Combine like terms: -40 + 40 = 0 0 + x = -40.249223595 + 40 x = -40.249223595 + 40 Combine like terms: -40.249223595 + 40 = -0.249223595 x = -0.249223595 Simplifying x = -0.249223595Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.249223595, -0.249223595}Solution
x = {80.249223595, -0.249223595}
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