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Simplifying 5x(x + -2) = 32 Reorder the terms: 5x(-2 + x) = 32 (-2 * 5x + x * 5x) = 32 (-10x + 5x2) = 32 Solving -10x + 5x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + -10x + 5x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + -2x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -2x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -2x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -2x + x2 = 0 + 6.4 -2x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -2x + x2 = 6.4 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 = 6.4 + 1 Reorder the terms: 1 + -2x + x2 = 6.4 + 1 Combine like terms: 6.4 + 1 = 7.4 1 + -2x + x2 = 7.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.4 Calculate the square root of the right side: 2.720294102 Break this problem into two subproblems by setting (x + -1) equal to 2.720294102 and -2.720294102.Subproblem 1
x + -1 = 2.720294102 Simplifying x + -1 = 2.720294102 Reorder the terms: -1 + x = 2.720294102 Solving -1 + x = 2.720294102 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 = 2.720294102 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.720294102 + 1 x = 2.720294102 + 1 Combine like terms: 2.720294102 + 1 = 3.720294102 x = 3.720294102 Simplifying x = 3.720294102Subproblem 2
x + -1 = -2.720294102 Simplifying x + -1 = -2.720294102 Reorder the terms: -1 + x = -2.720294102 Solving -1 + x = -2.720294102 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 = -2.720294102 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.720294102 + 1 x = -2.720294102 + 1 Combine like terms: -2.720294102 + 1 = -1.720294102 x = -1.720294102 Simplifying x = -1.720294102Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.720294102, -1.720294102}
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