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Simplifying -5x2 + -20x + -16 = 0 Reorder the terms: -16 + -20x + -5x2 = 0 Solving -16 + -20x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 20x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying 16 + 20x + 5x2 = 0 Solving 16 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + 4x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + 4x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + 4x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + 4x + x2 = 0 + -3.2 4x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 4x + x2 = -3.2 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 = -3.2 + 4 Reorder the terms: 4 + 4x + x2 = -3.2 + 4 Combine like terms: -3.2 + 4 = 0.8 4 + 4x + x2 = 0.8 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + 2) equal to 0.894427191 and -0.894427191.Subproblem 1
x + 2 = 0.894427191 Simplifying x + 2 = 0.894427191 Reorder the terms: 2 + x = 0.894427191 Solving 2 + x = 0.894427191 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 = 0.894427191 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.894427191 + -2 x = 0.894427191 + -2 Combine like terms: 0.894427191 + -2 = -1.105572809 x = -1.105572809 Simplifying x = -1.105572809Subproblem 2
x + 2 = -0.894427191 Simplifying x + 2 = -0.894427191 Reorder the terms: 2 + x = -0.894427191 Solving 2 + x = -0.894427191 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 = -0.894427191 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.894427191 + -2 x = -0.894427191 + -2 Combine like terms: -0.894427191 + -2 = -2.894427191 x = -2.894427191 Simplifying x = -2.894427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.105572809, -2.894427191}Solution
x = {-1.105572809, -2.894427191}
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