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Simplifying (2x + -5)(x + 4) + -20 = 0 Reorder the terms: (-5 + 2x)(x + 4) + -20 = 0 Reorder the terms: (-5 + 2x)(4 + x) + -20 = 0 Multiply (-5 + 2x) * (4 + x) (-5(4 + x) + 2x * (4 + x)) + -20 = 0 ((4 * -5 + x * -5) + 2x * (4 + x)) + -20 = 0 ((-20 + -5x) + 2x * (4 + x)) + -20 = 0 (-20 + -5x + (4 * 2x + x * 2x)) + -20 = 0 (-20 + -5x + (8x + 2x2)) + -20 = 0 Combine like terms: -5x + 8x = 3x (-20 + 3x + 2x2) + -20 = 0 Reorder the terms: -20 + -20 + 3x + 2x2 = 0 Combine like terms: -20 + -20 = -40 -40 + 3x + 2x2 = 0 Solving -40 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + 1.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.5x + x2 = 0 + 20 1.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.5x + x2 = 20 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 20 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 20 + 0.5625 Combine like terms: 20 + 0.5625 = 20.5625 0.5625 + 1.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 0.75) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 0.75 = 4.534589287 Simplifying x + 0.75 = 4.534589287 Reorder the terms: 0.75 + x = 4.534589287 Solving 0.75 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.534589287 + -0.75 x = 4.534589287 + -0.75 Combine like terms: 4.534589287 + -0.75 = 3.784589287 x = 3.784589287 Simplifying x = 3.784589287Subproblem 2
x + 0.75 = -4.534589287 Simplifying x + 0.75 = -4.534589287 Reorder the terms: 0.75 + x = -4.534589287 Solving 0.75 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.534589287 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.534589287 + -0.75 x = -4.534589287 + -0.75 Combine like terms: -4.534589287 + -0.75 = -5.284589287 x = -5.284589287 Simplifying x = -5.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.784589287, -5.284589287}
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