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Simplifying -2x2 + 160x + 800 = 0 Reorder the terms: 800 + 160x + -2x2 = 0 Solving 800 + 160x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(400 + 80x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(400 + 80x + -1x2)' equal to zero and attempt to solve: Simplifying 400 + 80x + -1x2 = 0 Solving 400 + 80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + -80x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -80x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -80x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -80x + x2 = 0 + 400 -80x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -80x + x2 = 400 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 = 400 + 1600 Reorder the terms: 1600 + -80x + x2 = 400 + 1600 Combine like terms: 400 + 1600 = 2000 1600 + -80x + x2 = 2000 Factor a perfect square on the left side: (x + -40)(x + -40) = 2000 Calculate the square root of the right side: 44.72135955 Break this problem into two subproblems by setting (x + -40) equal to 44.72135955 and -44.72135955.Subproblem 1
x + -40 = 44.72135955 Simplifying x + -40 = 44.72135955 Reorder the terms: -40 + x = 44.72135955 Solving -40 + x = 44.72135955 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 = 44.72135955 + 40 Combine like terms: -40 + 40 = 0 0 + x = 44.72135955 + 40 x = 44.72135955 + 40 Combine like terms: 44.72135955 + 40 = 84.72135955 x = 84.72135955 Simplifying x = 84.72135955Subproblem 2
x + -40 = -44.72135955 Simplifying x + -40 = -44.72135955 Reorder the terms: -40 + x = -44.72135955 Solving -40 + x = -44.72135955 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 = -44.72135955 + 40 Combine like terms: -40 + 40 = 0 0 + x = -44.72135955 + 40 x = -44.72135955 + 40 Combine like terms: -44.72135955 + 40 = -4.72135955 x = -4.72135955 Simplifying x = -4.72135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.72135955, -4.72135955}Solution
x = {84.72135955, -4.72135955}
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