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Simplifying 20 = 4x(x + -2) Reorder the terms: 20 = 4x(-2 + x) 20 = (-2 * 4x + x * 4x) 20 = (-8x + 4x2) Solving 20 = -8x + 4x2 Solving for variable 'x'. Reorder the terms: 20 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 20 + 8x + -4x2 = 0 + 4x2 + -4x2 20 + 8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 20 + 8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 2x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + -1x2 = 0 Solving 5 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -2x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + x2 = 0 + 5 -2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + x2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x + x2 = 6 Factor a perfect square on the left side: (x + -1)(x + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -1 = 2.449489743 Simplifying x + -1 = 2.449489743 Reorder the terms: -1 + x = 2.449489743 Solving -1 + x = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.449489743 + 1 x = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x = 3.449489743 Simplifying x = 3.449489743Subproblem 2
x + -1 = -2.449489743 Simplifying x + -1 = -2.449489743 Reorder the terms: -1 + x = -2.449489743 Solving -1 + x = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.449489743 + 1 x = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x = -1.449489743 Simplifying x = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.449489743, -1.449489743}Solution
x = {3.449489743, -1.449489743}
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