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Simplifying (-40x2) + -80x + -8 = 0 Reorder the terms: -8 + -80x + (-40x2) = 0 Solving -8 + -80x + (-40x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-8'. -8(1 + 10x + (5x2)) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(1 + 10x + (5x2))' equal to zero and attempt to solve: Simplifying 1 + 10x + (5x2) = 0 Solving 1 + 10x + (5x2) = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2x + x2 = 0 + -0.2 2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2x + x2 = -0.2 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 = -0.2 + 1 Reorder the terms: 1 + 2x + x2 = -0.2 + 1 Combine like terms: -0.2 + 1 = 0.8 1 + 2x + x2 = 0.8 Factor a perfect square on the left side: ((x) + 1)((x) + 1) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting ((x) + 1) equal to 0.894427191 and -0.894427191.Subproblem 1
(x) + 1 = 0.894427191 Simplifying (x) + 1 = 0.894427191 x + 1 = 0.894427191 Reorder the terms: 1 + x = 0.894427191 Solving 1 + x = 0.894427191 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 = 0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.894427191 + -1 x = 0.894427191 + -1 Combine like terms: 0.894427191 + -1 = -0.105572809 x = -0.105572809 Simplifying x = -0.105572809Subproblem 2
(x) + 1 = -0.894427191 Simplifying (x) + 1 = -0.894427191 x + 1 = -0.894427191 Reorder the terms: 1 + x = -0.894427191 Solving 1 + x = -0.894427191 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 = -0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.894427191 + -1 x = -0.894427191 + -1 Combine like terms: -0.894427191 + -1 = -1.894427191 x = -1.894427191 Simplifying x = -1.894427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.105572809, -1.894427191}Solution
x = {-0.105572809, -1.894427191}
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