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Simplifying (3 + 2x)(-2x + 3) = (1x + -2) Reorder the terms: (3 + 2x)(3 + -2x) = (1x + -2) Multiply (3 + 2x) * (3 + -2x) (3(3 + -2x) + 2x * (3 + -2x)) = (1x + -2) ((3 * 3 + -2x * 3) + 2x * (3 + -2x)) = (1x + -2) ((9 + -6x) + 2x * (3 + -2x)) = (1x + -2) (9 + -6x + (3 * 2x + -2x * 2x)) = (1x + -2) (9 + -6x + (6x + -4x2)) = (1x + -2) Combine like terms: -6x + 6x = 0 (9 + 0 + -4x2) = (1x + -2) (9 + -4x2) = (1x + -2) Reorder the terms: 9 + -4x2 = (-2 + 1x) Remove parenthesis around (-2 + 1x) 9 + -4x2 = -2 + 1x Solving 9 + -4x2 = -2 + 1x Solving for variable 'x'. Reorder the terms: 9 + 2 + -1x + -4x2 = -2 + 1x + 2 + -1x Combine like terms: 9 + 2 = 11 11 + -1x + -4x2 = -2 + 1x + 2 + -1x Reorder the terms: 11 + -1x + -4x2 = -2 + 2 + 1x + -1x Combine like terms: -2 + 2 = 0 11 + -1x + -4x2 = 0 + 1x + -1x 11 + -1x + -4x2 = 1x + -1x Combine like terms: 1x + -1x = 0 11 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 0.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 0.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 0.25x + x2 = 0 + 2.75 0.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 0.25x + x2 = 2.75 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 2.75 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 2.75 + 0.015625 Combine like terms: 2.75 + 0.015625 = 2.765625 0.015625 + 0.25x + x2 = 2.765625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 2.765625 Calculate the square root of the right side: 1.663016837 Break this problem into two subproblems by setting (x + 0.125) equal to 1.663016837 and -1.663016837.Subproblem 1
x + 0.125 = 1.663016837 Simplifying x + 0.125 = 1.663016837 Reorder the terms: 0.125 + x = 1.663016837 Solving 0.125 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.663016837 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.663016837 + -0.125 x = 1.663016837 + -0.125 Combine like terms: 1.663016837 + -0.125 = 1.538016837 x = 1.538016837 Simplifying x = 1.538016837Subproblem 2
x + 0.125 = -1.663016837 Simplifying x + 0.125 = -1.663016837 Reorder the terms: 0.125 + x = -1.663016837 Solving 0.125 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.663016837 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.663016837 + -0.125 x = -1.663016837 + -0.125 Combine like terms: -1.663016837 + -0.125 = -1.788016837 x = -1.788016837 Simplifying x = -1.788016837Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.538016837, -1.788016837}
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