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Simplifying (2x + -3)(x + -3) = 476 Reorder the terms: (-3 + 2x)(x + -3) = 476 Reorder the terms: (-3 + 2x)(-3 + x) = 476 Multiply (-3 + 2x) * (-3 + x) (-3(-3 + x) + 2x * (-3 + x)) = 476 ((-3 * -3 + x * -3) + 2x * (-3 + x)) = 476 ((9 + -3x) + 2x * (-3 + x)) = 476 (9 + -3x + (-3 * 2x + x * 2x)) = 476 (9 + -3x + (-6x + 2x2)) = 476 Combine like terms: -3x + -6x = -9x (9 + -9x + 2x2) = 476 Solving 9 + -9x + 2x2 = 476 Solving for variable 'x'. Reorder the terms: 9 + -476 + -9x + 2x2 = 476 + -476 Combine like terms: 9 + -476 = -467 -467 + -9x + 2x2 = 476 + -476 Combine like terms: 476 + -476 = 0 -467 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -233.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '233.5' to each side of the equation. -233.5 + -4.5x + 233.5 + x2 = 0 + 233.5 Reorder the terms: -233.5 + 233.5 + -4.5x + x2 = 0 + 233.5 Combine like terms: -233.5 + 233.5 = 0.0 0.0 + -4.5x + x2 = 0 + 233.5 -4.5x + x2 = 0 + 233.5 Combine like terms: 0 + 233.5 = 233.5 -4.5x + x2 = 233.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 233.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 233.5 + 5.0625 Combine like terms: 233.5 + 5.0625 = 238.5625 5.0625 + -4.5x + x2 = 238.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 238.5625 Calculate the square root of the right side: 15.445468591 Break this problem into two subproblems by setting (x + -2.25) equal to 15.445468591 and -15.445468591.Subproblem 1
x + -2.25 = 15.445468591 Simplifying x + -2.25 = 15.445468591 Reorder the terms: -2.25 + x = 15.445468591 Solving -2.25 + x = 15.445468591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 15.445468591 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 15.445468591 + 2.25 x = 15.445468591 + 2.25 Combine like terms: 15.445468591 + 2.25 = 17.695468591 x = 17.695468591 Simplifying x = 17.695468591Subproblem 2
x + -2.25 = -15.445468591 Simplifying x + -2.25 = -15.445468591 Reorder the terms: -2.25 + x = -15.445468591 Solving -2.25 + x = -15.445468591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -15.445468591 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -15.445468591 + 2.25 x = -15.445468591 + 2.25 Combine like terms: -15.445468591 + 2.25 = -13.195468591 x = -13.195468591 Simplifying x = -13.195468591Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.695468591, -13.195468591}
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