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Simplifying (2x + -3)(2x + -3) = 2x Reorder the terms: (-3 + 2x)(2x + -3) = 2x Reorder the terms: (-3 + 2x)(-3 + 2x) = 2x Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) = 2x ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 2x ((9 + -6x) + 2x * (-3 + 2x)) = 2x (9 + -6x + (-3 * 2x + 2x * 2x)) = 2x (9 + -6x + (-6x + 4x2)) = 2x Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) = 2x Solving 9 + -12x + 4x2 = 2x Solving for variable 'x'. Reorder the terms: 9 + -12x + -2x + 4x2 = 2x + -2x Combine like terms: -12x + -2x = -14x 9 + -14x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 9 + -14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -3.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -3.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3.5x + x2 = 0 + -2.25 -3.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -3.5x + x2 = -2.25 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -2.25 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -2.25 + 3.0625 Combine like terms: -2.25 + 3.0625 = 0.8125 3.0625 + -3.5x + x2 = 0.8125 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + -1.75) equal to 0.901387819 and -0.901387819.Subproblem 1
x + -1.75 = 0.901387819 Simplifying x + -1.75 = 0.901387819 Reorder the terms: -1.75 + x = 0.901387819 Solving -1.75 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 0.901387819 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.901387819 + 1.75 x = 0.901387819 + 1.75 Combine like terms: 0.901387819 + 1.75 = 2.651387819 x = 2.651387819 Simplifying x = 2.651387819Subproblem 2
x + -1.75 = -0.901387819 Simplifying x + -1.75 = -0.901387819 Reorder the terms: -1.75 + x = -0.901387819 Solving -1.75 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -0.901387819 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -0.901387819 + 1.75 x = -0.901387819 + 1.75 Combine like terms: -0.901387819 + 1.75 = 0.848612181 x = 0.848612181 Simplifying x = 0.848612181Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.651387819, 0.848612181}
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