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Simplifying (5x + -1)(2x + -4) = 9 Reorder the terms: (-1 + 5x)(2x + -4) = 9 Reorder the terms: (-1 + 5x)(-4 + 2x) = 9 Multiply (-1 + 5x) * (-4 + 2x) (-1(-4 + 2x) + 5x * (-4 + 2x)) = 9 ((-4 * -1 + 2x * -1) + 5x * (-4 + 2x)) = 9 ((4 + -2x) + 5x * (-4 + 2x)) = 9 (4 + -2x + (-4 * 5x + 2x * 5x)) = 9 (4 + -2x + (-20x + 10x2)) = 9 Combine like terms: -2x + -20x = -22x (4 + -22x + 10x2) = 9 Solving 4 + -22x + 10x2 = 9 Solving for variable 'x'. Reorder the terms: 4 + -9 + -22x + 10x2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + -22x + 10x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + -22x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -2.2x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.2x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.2x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.2x + x2 = 0.0 + 0.5 -2.2x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -2.2x + x2 = 0.5 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 0.5 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 0.5 + 1.21 Combine like terms: 0.5 + 1.21 = 1.71 1.21 + -2.2x + x2 = 1.71 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 1.71 Calculate the square root of the right side: 1.307669683 Break this problem into two subproblems by setting (x + -1.1) equal to 1.307669683 and -1.307669683.Subproblem 1
x + -1.1 = 1.307669683 Simplifying x + -1.1 = 1.307669683 Reorder the terms: -1.1 + x = 1.307669683 Solving -1.1 + x = 1.307669683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.307669683 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.307669683 + 1.1 x = 1.307669683 + 1.1 Combine like terms: 1.307669683 + 1.1 = 2.407669683 x = 2.407669683 Simplifying x = 2.407669683Subproblem 2
x + -1.1 = -1.307669683 Simplifying x + -1.1 = -1.307669683 Reorder the terms: -1.1 + x = -1.307669683 Solving -1.1 + x = -1.307669683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.307669683 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.307669683 + 1.1 x = -1.307669683 + 1.1 Combine like terms: -1.307669683 + 1.1 = -0.207669683 x = -0.207669683 Simplifying x = -0.207669683Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.407669683, -0.207669683}
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