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Simplifying (2x + -3)(x + 3) = 3 Reorder the terms: (-3 + 2x)(x + 3) = 3 Reorder the terms: (-3 + 2x)(3 + x) = 3 Multiply (-3 + 2x) * (3 + x) (-3(3 + x) + 2x * (3 + x)) = 3 ((3 * -3 + x * -3) + 2x * (3 + x)) = 3 ((-9 + -3x) + 2x * (3 + x)) = 3 (-9 + -3x + (3 * 2x + x * 2x)) = 3 (-9 + -3x + (6x + 2x2)) = 3 Combine like terms: -3x + 6x = 3x (-9 + 3x + 2x2) = 3 Solving -9 + 3x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -9 + -3 + 3x + 2x2 = 3 + -3 Combine like terms: -9 + -3 = -12 -12 + 3x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -12 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 1.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.5x + x2 = 0 + 6 1.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.5x + x2 = 6 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 6 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 6 + 0.5625 Combine like terms: 6 + 0.5625 = 6.5625 0.5625 + 1.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + 0.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + 0.75 = 2.561737691 Simplifying x + 0.75 = 2.561737691 Reorder the terms: 0.75 + x = 2.561737691 Solving 0.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.561737691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.561737691 + -0.75 x = 2.561737691 + -0.75 Combine like terms: 2.561737691 + -0.75 = 1.811737691 x = 1.811737691 Simplifying x = 1.811737691Subproblem 2
x + 0.75 = -2.561737691 Simplifying x + 0.75 = -2.561737691 Reorder the terms: 0.75 + x = -2.561737691 Solving 0.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.561737691 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.561737691 + -0.75 x = -2.561737691 + -0.75 Combine like terms: -2.561737691 + -0.75 = -3.311737691 x = -3.311737691 Simplifying x = -3.311737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.811737691, -3.311737691}
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