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Simplifying (0.3 + 2x)(0.4 + 2x) = 4.08 Multiply (0.3 + 2x) * (0.4 + 2x) (0.3(0.4 + 2x) + 2x * (0.4 + 2x)) = 4.08 ((0.4 * 0.3 + 2x * 0.3) + 2x * (0.4 + 2x)) = 4.08 ((0.12 + 0.6x) + 2x * (0.4 + 2x)) = 4.08 (0.12 + 0.6x + (0.4 * 2x + 2x * 2x)) = 4.08 (0.12 + 0.6x + (0.8x + 4x2)) = 4.08 Combine like terms: 0.6x + 0.8x = 1.4x (0.12 + 1.4x + 4x2) = 4.08 Solving 0.12 + 1.4x + 4x2 = 4.08 Solving for variable 'x'. Reorder the terms: 0.12 + -4.08 + 1.4x + 4x2 = 4.08 + -4.08 Combine like terms: 0.12 + -4.08 = -3.96 -3.96 + 1.4x + 4x2 = 4.08 + -4.08 Combine like terms: 4.08 + -4.08 = 0.00 -3.96 + 1.4x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.99 + 0.35x + x2 = 0.00 Move the constant term to the right: Add '0.99' to each side of the equation. -0.99 + 0.35x + 0.99 + x2 = 0.00 + 0.99 Reorder the terms: -0.99 + 0.99 + 0.35x + x2 = 0.00 + 0.99 Combine like terms: -0.99 + 0.99 = 0.00 0.00 + 0.35x + x2 = 0.00 + 0.99 0.35x + x2 = 0.00 + 0.99 Combine like terms: 0.00 + 0.99 = 0.99 0.35x + x2 = 0.99 The x term is 0.35x. Take half its coefficient (0.175). Square it (0.030625) and add it to both sides. Add '0.030625' to each side of the equation. 0.35x + 0.030625 + x2 = 0.99 + 0.030625 Reorder the terms: 0.030625 + 0.35x + x2 = 0.99 + 0.030625 Combine like terms: 0.99 + 0.030625 = 1.020625 0.030625 + 0.35x + x2 = 1.020625 Factor a perfect square on the left side: (x + 0.175)(x + 0.175) = 1.020625 Calculate the square root of the right side: 1.010259868 Break this problem into two subproblems by setting (x + 0.175) equal to 1.010259868 and -1.010259868.Subproblem 1
x + 0.175 = 1.010259868 Simplifying x + 0.175 = 1.010259868 Reorder the terms: 0.175 + x = 1.010259868 Solving 0.175 + x = 1.010259868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = 1.010259868 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = 1.010259868 + -0.175 x = 1.010259868 + -0.175 Combine like terms: 1.010259868 + -0.175 = 0.835259868 x = 0.835259868 Simplifying x = 0.835259868Subproblem 2
x + 0.175 = -1.010259868 Simplifying x + 0.175 = -1.010259868 Reorder the terms: 0.175 + x = -1.010259868 Solving 0.175 + x = -1.010259868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.175' to each side of the equation. 0.175 + -0.175 + x = -1.010259868 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + x = -1.010259868 + -0.175 x = -1.010259868 + -0.175 Combine like terms: -1.010259868 + -0.175 = -1.185259868 x = -1.185259868 Simplifying x = -1.185259868Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.835259868, -1.185259868}
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