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Simplifying (0.3 + 2x)(0.3 + 2x) = 3.266 Multiply (0.3 + 2x) * (0.3 + 2x) (0.3(0.3 + 2x) + 2x * (0.3 + 2x)) = 3.266 ((0.3 * 0.3 + 2x * 0.3) + 2x * (0.3 + 2x)) = 3.266 ((0.09 + 0.6x) + 2x * (0.3 + 2x)) = 3.266 (0.09 + 0.6x + (0.3 * 2x + 2x * 2x)) = 3.266 (0.09 + 0.6x + (0.6x + 4x2)) = 3.266 Combine like terms: 0.6x + 0.6x = 1.2x (0.09 + 1.2x + 4x2) = 3.266 Solving 0.09 + 1.2x + 4x2 = 3.266 Solving for variable 'x'. Reorder the terms: 0.09 + -3.266 + 1.2x + 4x2 = 3.266 + -3.266 Combine like terms: 0.09 + -3.266 = -3.176 -3.176 + 1.2x + 4x2 = 3.266 + -3.266 Combine like terms: 3.266 + -3.266 = 0.000 -3.176 + 1.2x + 4x2 = 0.000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.794 + 0.3x + x2 = 0.000 Move the constant term to the right: Add '0.794' to each side of the equation. -0.794 + 0.3x + 0.794 + x2 = 0.000 + 0.794 Reorder the terms: -0.794 + 0.794 + 0.3x + x2 = 0.000 + 0.794 Combine like terms: -0.794 + 0.794 = 0.000 0.000 + 0.3x + x2 = 0.000 + 0.794 0.3x + x2 = 0.000 + 0.794 Combine like terms: 0.000 + 0.794 = 0.794 0.3x + x2 = 0.794 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 0.794 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.794 + 0.0225 Combine like terms: 0.794 + 0.0225 = 0.8165 0.0225 + 0.3x + x2 = 0.8165 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.8165 Calculate the square root of the right side: 0.903603896 Break this problem into two subproblems by setting (x + 0.15) equal to 0.903603896 and -0.903603896.Subproblem 1
x + 0.15 = 0.903603896 Simplifying x + 0.15 = 0.903603896 Reorder the terms: 0.15 + x = 0.903603896 Solving 0.15 + x = 0.903603896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.903603896 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.903603896 + -0.15 x = 0.903603896 + -0.15 Combine like terms: 0.903603896 + -0.15 = 0.753603896 x = 0.753603896 Simplifying x = 0.753603896Subproblem 2
x + 0.15 = -0.903603896 Simplifying x + 0.15 = -0.903603896 Reorder the terms: 0.15 + x = -0.903603896 Solving 0.15 + x = -0.903603896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.903603896 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.903603896 + -0.15 x = -0.903603896 + -0.15 Combine like terms: -0.903603896 + -0.15 = -1.053603896 x = -1.053603896 Simplifying x = -1.053603896Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.753603896, -1.053603896}
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