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Simplifying (2x + -3)(2x + -3) = 26 Reorder the terms: (-3 + 2x)(2x + -3) = 26 Reorder the terms: (-3 + 2x)(-3 + 2x) = 26 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) = 26 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 26 ((9 + -6x) + 2x * (-3 + 2x)) = 26 (9 + -6x + (-3 * 2x + 2x * 2x)) = 26 (9 + -6x + (-6x + 4x2)) = 26 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) = 26 Solving 9 + -12x + 4x2 = 26 Solving for variable 'x'. Reorder the terms: 9 + -26 + -12x + 4x2 = 26 + -26 Combine like terms: 9 + -26 = -17 -17 + -12x + 4x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -17 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -3x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -3x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -3x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -3x + x2 = 0 + 4.25 -3x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -3x + x2 = 4.25 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 = 4.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4.25 + 2.25 Combine like terms: 4.25 + 2.25 = 6.5 2.25 + -3x + x2 = 6.5 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -1.5) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -1.5 = 2.549509757 Simplifying x + -1.5 = 2.549509757 Reorder the terms: -1.5 + x = 2.549509757 Solving -1.5 + x = 2.549509757 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 = 2.549509757 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.549509757 + 1.5 x = 2.549509757 + 1.5 Combine like terms: 2.549509757 + 1.5 = 4.049509757 x = 4.049509757 Simplifying x = 4.049509757Subproblem 2
x + -1.5 = -2.549509757 Simplifying x + -1.5 = -2.549509757 Reorder the terms: -1.5 + x = -2.549509757 Solving -1.5 + x = -2.549509757 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 = -2.549509757 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.549509757 + 1.5 x = -2.549509757 + 1.5 Combine like terms: -2.549509757 + 1.5 = -1.049509757 x = -1.049509757 Simplifying x = -1.049509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.049509757, -1.049509757}
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