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Simplifying (2x + -3)(2x + -3) + -9x + 6 = 0 Reorder the terms: (-3 + 2x)(2x + -3) + -9x + 6 = 0 Reorder the terms: (-3 + 2x)(-3 + 2x) + -9x + 6 = 0 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) + -9x + 6 = 0 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + -9x + 6 = 0 ((9 + -6x) + 2x * (-3 + 2x)) + -9x + 6 = 0 (9 + -6x + (-3 * 2x + 2x * 2x)) + -9x + 6 = 0 (9 + -6x + (-6x + 4x2)) + -9x + 6 = 0 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) + -9x + 6 = 0 Reorder the terms: 9 + 6 + -12x + -9x + 4x2 = 0 Combine like terms: 9 + 6 = 15 15 + -12x + -9x + 4x2 = 0 Combine like terms: -12x + -9x = -21x 15 + -21x + 4x2 = 0 Solving 15 + -21x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -5.25x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -5.25x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -5.25x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -5.25x + x2 = 0 + -3.75 -5.25x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -5.25x + x2 = -3.75 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -3.75 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -3.75 + 6.890625 Combine like terms: -3.75 + 6.890625 = 3.140625 6.890625 + -5.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -2.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -2.625 = 1.77218086 Simplifying x + -2.625 = 1.77218086 Reorder the terms: -2.625 + x = 1.77218086 Solving -2.625 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 1.77218086 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.77218086 + 2.625 x = 1.77218086 + 2.625 Combine like terms: 1.77218086 + 2.625 = 4.39718086 x = 4.39718086 Simplifying x = 4.39718086Subproblem 2
x + -2.625 = -1.77218086 Simplifying x + -2.625 = -1.77218086 Reorder the terms: -2.625 + x = -1.77218086 Solving -2.625 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -1.77218086 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.77218086 + 2.625 x = -1.77218086 + 2.625 Combine like terms: -1.77218086 + 2.625 = 0.85281914 x = 0.85281914 Simplifying x = 0.85281914Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.39718086, 0.85281914}
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