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Simplifying 20x2 + -40x + -16 = 0 Reorder the terms: -16 + -40x + 20x2 = 0 Solving -16 + -40x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -10x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -10x + 5x2)' equal to zero and attempt to solve: Simplifying -4 + -10x + 5x2 = 0 Solving -4 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -2x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -2x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -2x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -2x + x2 = 0 + 0.8 -2x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -2x + x2 = 0.8 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 = 0.8 + 1 Reorder the terms: 1 + -2x + x2 = 0.8 + 1 Combine like terms: 0.8 + 1 = 1.8 1 + -2x + x2 = 1.8 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.8 Calculate the square root of the right side: 1.341640787 Break this problem into two subproblems by setting (x + -1) equal to 1.341640787 and -1.341640787.Subproblem 1
x + -1 = 1.341640787 Simplifying x + -1 = 1.341640787 Reorder the terms: -1 + x = 1.341640787 Solving -1 + x = 1.341640787 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 = 1.341640787 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.341640787 + 1 x = 1.341640787 + 1 Combine like terms: 1.341640787 + 1 = 2.341640787 x = 2.341640787 Simplifying x = 2.341640787Subproblem 2
x + -1 = -1.341640787 Simplifying x + -1 = -1.341640787 Reorder the terms: -1 + x = -1.341640787 Solving -1 + x = -1.341640787 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 = -1.341640787 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.341640787 + 1 x = -1.341640787 + 1 Combine like terms: -1.341640787 + 1 = -0.341640787 x = -0.341640787 Simplifying x = -0.341640787Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.341640787, -0.341640787}Solution
x = {2.341640787, -0.341640787}
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