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Simplifying 0 = -5x2 + 20x + 80 Reorder the terms: 0 = 80 + 20x + -5x2 Solving 0 = 80 + 20x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + -20x + 5x2 = 80 + 20x + -5x2 + -80 + -20x + 5x2 Reorder the terms: -80 + -20x + 5x2 = 80 + -80 + 20x + -20x + -5x2 + 5x2 Combine like terms: 80 + -80 = 0 -80 + -20x + 5x2 = 0 + 20x + -20x + -5x2 + 5x2 -80 + -20x + 5x2 = 20x + -20x + -5x2 + 5x2 Combine like terms: 20x + -20x = 0 -80 + -20x + 5x2 = 0 + -5x2 + 5x2 -80 + -20x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -80 + -20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + -4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16 + -4x + x2)' equal to zero and attempt to solve: Simplifying -16 + -4x + x2 = 0 Solving -16 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -4x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -4x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4x + x2 = 0 + 16 -4x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -4x + x2 = 16 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 16 + 4 Reorder the terms: 4 + -4x + x2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + -4x + x2 = 20 Factor a perfect square on the left side: (x + -2)(x + -2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -2) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -2 = 4.472135955 Simplifying x + -2 = 4.472135955 Reorder the terms: -2 + x = 4.472135955 Solving -2 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.472135955 + 2 x = 4.472135955 + 2 Combine like terms: 4.472135955 + 2 = 6.472135955 x = 6.472135955 Simplifying x = 6.472135955Subproblem 2
x + -2 = -4.472135955 Simplifying x + -2 = -4.472135955 Reorder the terms: -2 + x = -4.472135955 Solving -2 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.472135955 + 2 x = -4.472135955 + 2 Combine like terms: -4.472135955 + 2 = -2.472135955 x = -2.472135955 Simplifying x = -2.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.472135955, -2.472135955}Solution
x = {6.472135955, -2.472135955}
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