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Simplifying 0 = -5x2 + 50x + 80 Reorder the terms: 0 = 80 + 50x + -5x2 Solving 0 = 80 + 50x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + -50x + 5x2 = 80 + 50x + -5x2 + -80 + -50x + 5x2 Reorder the terms: -80 + -50x + 5x2 = 80 + -80 + 50x + -50x + -5x2 + 5x2 Combine like terms: 80 + -80 = 0 -80 + -50x + 5x2 = 0 + 50x + -50x + -5x2 + 5x2 -80 + -50x + 5x2 = 50x + -50x + -5x2 + 5x2 Combine like terms: 50x + -50x = 0 -80 + -50x + 5x2 = 0 + -5x2 + 5x2 -80 + -50x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -80 + -50x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + -10x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16 + -10x + x2)' equal to zero and attempt to solve: Simplifying -16 + -10x + x2 = 0 Solving -16 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -10x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -10x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -10x + x2 = 0 + 16 -10x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -10x + x2 = 16 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 = 16 + 25 Reorder the terms: 25 + -10x + x2 = 16 + 25 Combine like terms: 16 + 25 = 41 25 + -10x + x2 = 41 Factor a perfect square on the left side: (x + -5)(x + -5) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -5) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -5 = 6.403124237 Simplifying x + -5 = 6.403124237 Reorder the terms: -5 + x = 6.403124237 Solving -5 + x = 6.403124237 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 = 6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.403124237 + 5 x = 6.403124237 + 5 Combine like terms: 6.403124237 + 5 = 11.403124237 x = 11.403124237 Simplifying x = 11.403124237Subproblem 2
x + -5 = -6.403124237 Simplifying x + -5 = -6.403124237 Reorder the terms: -5 + x = -6.403124237 Solving -5 + x = -6.403124237 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 = -6.403124237 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.403124237 + 5 x = -6.403124237 + 5 Combine like terms: -6.403124237 + 5 = -1.403124237 x = -1.403124237 Simplifying x = -1.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.403124237, -1.403124237}Solution
x = {11.403124237, -1.403124237}
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