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Simplifying (2 + -2x)(4 + -2x) = 9.5 Multiply (2 + -2x) * (4 + -2x) (2(4 + -2x) + -2x * (4 + -2x)) = 9.5 ((4 * 2 + -2x * 2) + -2x * (4 + -2x)) = 9.5 ((8 + -4x) + -2x * (4 + -2x)) = 9.5 (8 + -4x + (4 * -2x + -2x * -2x)) = 9.5 (8 + -4x + (-8x + 4x2)) = 9.5 Combine like terms: -4x + -8x = -12x (8 + -12x + 4x2) = 9.5 Solving 8 + -12x + 4x2 = 9.5 Solving for variable 'x'. Reorder the terms: 8 + -9.5 + -12x + 4x2 = 9.5 + -9.5 Combine like terms: 8 + -9.5 = -1.5 -1.5 + -12x + 4x2 = 9.5 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 -1.5 + -12x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.375 + -3x + x2 = 0.0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3x + 0.375 + x2 = 0.0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3x + x2 = 0.0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3x + x2 = 0.0 + 0.375 -3x + x2 = 0.0 + 0.375 Combine like terms: 0.0 + 0.375 = 0.375 -3x + x2 = 0.375 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.375 + 2.25 Combine like terms: 0.375 + 2.25 = 2.625 2.25 + -3x + x2 = 2.625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (x + -1.5) equal to 1.620185175 and -1.620185175.Subproblem 1
x + -1.5 = 1.620185175 Simplifying x + -1.5 = 1.620185175 Reorder the terms: -1.5 + x = 1.620185175 Solving -1.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.620185175 + 1.5 x = 1.620185175 + 1.5 Combine like terms: 1.620185175 + 1.5 = 3.120185175 x = 3.120185175 Simplifying x = 3.120185175Subproblem 2
x + -1.5 = -1.620185175 Simplifying x + -1.5 = -1.620185175 Reorder the terms: -1.5 + x = -1.620185175 Solving -1.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.620185175 + 1.5 x = -1.620185175 + 1.5 Combine like terms: -1.620185175 + 1.5 = -0.120185175 x = -0.120185175 Simplifying x = -0.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.120185175, -0.120185175}
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