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Simplifying 8.85x(2 + x) = (3.8 + -2x)(3.8 + -2x) (2 * 8.85x + x * 8.85x) = (3.8 + -2x)(3.8 + -2x) (17.7x + 8.85x2) = (3.8 + -2x)(3.8 + -2x) Multiply (3.8 + -2x) * (3.8 + -2x) 17.7x + 8.85x2 = (3.8(3.8 + -2x) + -2x * (3.8 + -2x)) 17.7x + 8.85x2 = ((3.8 * 3.8 + -2x * 3.8) + -2x * (3.8 + -2x)) 17.7x + 8.85x2 = ((14.44 + -7.6x) + -2x * (3.8 + -2x)) 17.7x + 8.85x2 = (14.44 + -7.6x + (3.8 * -2x + -2x * -2x)) 17.7x + 8.85x2 = (14.44 + -7.6x + (-7.6x + 4x2)) Combine like terms: -7.6x + -7.6x = -15.2x 17.7x + 8.85x2 = (14.44 + -15.2x + 4x2) Solving 17.7x + 8.85x2 = 14.44 + -15.2x + 4x2 Solving for variable 'x'. Reorder the terms: -14.44 + 17.7x + 15.2x + 8.85x2 + -4x2 = 14.44 + -15.2x + 4x2 + -14.44 + 15.2x + -4x2 Combine like terms: 17.7x + 15.2x = 32.9x -14.44 + 32.9x + 8.85x2 + -4x2 = 14.44 + -15.2x + 4x2 + -14.44 + 15.2x + -4x2 Combine like terms: 8.85x2 + -4x2 = 4.85x2 -14.44 + 32.9x + 4.85x2 = 14.44 + -15.2x + 4x2 + -14.44 + 15.2x + -4x2 Reorder the terms: -14.44 + 32.9x + 4.85x2 = 14.44 + -14.44 + -15.2x + 15.2x + 4x2 + -4x2 Combine like terms: 14.44 + -14.44 = 0.00 -14.44 + 32.9x + 4.85x2 = 0.00 + -15.2x + 15.2x + 4x2 + -4x2 -14.44 + 32.9x + 4.85x2 = -15.2x + 15.2x + 4x2 + -4x2 Combine like terms: -15.2x + 15.2x = 0.0 -14.44 + 32.9x + 4.85x2 = 0.0 + 4x2 + -4x2 -14.44 + 32.9x + 4.85x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -14.44 + 32.9x + 4.85x2 = 0 Begin completing the square. Divide all terms by 4.85 the coefficient of the squared term: Divide each side by '4.85'. -2.977319588 + 6.783505155x + x2 = 0 Move the constant term to the right: Add '2.977319588' to each side of the equation. -2.977319588 + 6.783505155x + 2.977319588 + x2 = 0 + 2.977319588 Reorder the terms: -2.977319588 + 2.977319588 + 6.783505155x + x2 = 0 + 2.977319588 Combine like terms: -2.977319588 + 2.977319588 = 0.000000000 0.000000000 + 6.783505155x + x2 = 0 + 2.977319588 6.783505155x + x2 = 0 + 2.977319588 Combine like terms: 0 + 2.977319588 = 2.977319588 6.783505155x + x2 = 2.977319588 The x term is 6.783505155x. Take half its coefficient (3.391752578). Square it (11.50398555) and add it to both sides. Add '11.50398555' to each side of the equation. 6.783505155x + 11.50398555 + x2 = 2.977319588 + 11.50398555 Reorder the terms: 11.50398555 + 6.783505155x + x2 = 2.977319588 + 11.50398555 Combine like terms: 2.977319588 + 11.50398555 = 14.481305138 11.50398555 + 6.783505155x + x2 = 14.481305138 Factor a perfect square on the left side: (x + 3.391752578)(x + 3.391752578) = 14.481305138 Calculate the square root of the right side: 3.805431006 Break this problem into two subproblems by setting (x + 3.391752578) equal to 3.805431006 and -3.805431006.Subproblem 1
x + 3.391752578 = 3.805431006 Simplifying x + 3.391752578 = 3.805431006 Reorder the terms: 3.391752578 + x = 3.805431006 Solving 3.391752578 + x = 3.805431006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.391752578' to each side of the equation. 3.391752578 + -3.391752578 + x = 3.805431006 + -3.391752578 Combine like terms: 3.391752578 + -3.391752578 = 0.000000000 0.000000000 + x = 3.805431006 + -3.391752578 x = 3.805431006 + -3.391752578 Combine like terms: 3.805431006 + -3.391752578 = 0.413678428 x = 0.413678428 Simplifying x = 0.413678428Subproblem 2
x + 3.391752578 = -3.805431006 Simplifying x + 3.391752578 = -3.805431006 Reorder the terms: 3.391752578 + x = -3.805431006 Solving 3.391752578 + x = -3.805431006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.391752578' to each side of the equation. 3.391752578 + -3.391752578 + x = -3.805431006 + -3.391752578 Combine like terms: 3.391752578 + -3.391752578 = 0.000000000 0.000000000 + x = -3.805431006 + -3.391752578 x = -3.805431006 + -3.391752578 Combine like terms: -3.805431006 + -3.391752578 = -7.197183584 x = -7.197183584 Simplifying x = -7.197183584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.413678428, -7.197183584}
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