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Simplifying 20x2 + -128x = 4 Reorder the terms: -128x + 20x2 = 4 Solving -128x + 20x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -128x + 20x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -128x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -32x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -32x + 5x2)' equal to zero and attempt to solve: Simplifying -1 + -32x + 5x2 = 0 Solving -1 + -32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -6.4x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -6.4x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -6.4x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -6.4x + x2 = 0 + 0.2 -6.4x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -6.4x + x2 = 0.2 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 0.2 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 0.2 + 10.24 Combine like terms: 0.2 + 10.24 = 10.44 10.24 + -6.4x + x2 = 10.44 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 10.44 Calculate the square root of the right side: 3.231098884 Break this problem into two subproblems by setting (x + -3.2) equal to 3.231098884 and -3.231098884.Subproblem 1
x + -3.2 = 3.231098884 Simplifying x + -3.2 = 3.231098884 Reorder the terms: -3.2 + x = 3.231098884 Solving -3.2 + x = 3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 3.231098884 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.231098884 + 3.2 x = 3.231098884 + 3.2 Combine like terms: 3.231098884 + 3.2 = 6.431098884 x = 6.431098884 Simplifying x = 6.431098884Subproblem 2
x + -3.2 = -3.231098884 Simplifying x + -3.2 = -3.231098884 Reorder the terms: -3.2 + x = -3.231098884 Solving -3.2 + x = -3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -3.231098884 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.231098884 + 3.2 x = -3.231098884 + 3.2 Combine like terms: -3.231098884 + 3.2 = -0.031098884 x = -0.031098884 Simplifying x = -0.031098884Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.431098884, -0.031098884}Solution
x = {6.431098884, -0.031098884}
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