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Simplifying (5x + -1)(2x + 4) = 9x Reorder the terms: (-1 + 5x)(2x + 4) = 9x Reorder the terms: (-1 + 5x)(4 + 2x) = 9x Multiply (-1 + 5x) * (4 + 2x) (-1(4 + 2x) + 5x * (4 + 2x)) = 9x ((4 * -1 + 2x * -1) + 5x * (4 + 2x)) = 9x ((-4 + -2x) + 5x * (4 + 2x)) = 9x (-4 + -2x + (4 * 5x + 2x * 5x)) = 9x (-4 + -2x + (20x + 10x2)) = 9x Combine like terms: -2x + 20x = 18x (-4 + 18x + 10x2) = 9x Solving -4 + 18x + 10x2 = 9x Solving for variable 'x'. Reorder the terms: -4 + 18x + -9x + 10x2 = 9x + -9x Combine like terms: 18x + -9x = 9x -4 + 9x + 10x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -4 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + 0.9x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.9x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.9x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.9x + x2 = 0.0 + 0.4 0.9x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 0.9x + x2 = 0.4 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 0.4 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 0.4 + 0.2025 Combine like terms: 0.4 + 0.2025 = 0.6025 0.2025 + 0.9x + x2 = 0.6025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + 0.45) equal to 0.776208735 and -0.776208735.Subproblem 1
x + 0.45 = 0.776208735 Simplifying x + 0.45 = 0.776208735 Reorder the terms: 0.45 + x = 0.776208735 Solving 0.45 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 0.776208735 + -0.45 x = 0.776208735 + -0.45 Combine like terms: 0.776208735 + -0.45 = 0.326208735 x = 0.326208735 Simplifying x = 0.326208735Subproblem 2
x + 0.45 = -0.776208735 Simplifying x + 0.45 = -0.776208735 Reorder the terms: 0.45 + x = -0.776208735 Solving 0.45 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -0.776208735 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -0.776208735 + -0.45 x = -0.776208735 + -0.45 Combine like terms: -0.776208735 + -0.45 = -1.226208735 x = -1.226208735 Simplifying x = -1.226208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326208735, -1.226208735}
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