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Simplifying (x + -4.5)(x + 3.3) = 0 Reorder the terms: (-4.5 + x)(x + 3.3) = 0 Reorder the terms: (-4.5 + x)(3.3 + x) = 0 Multiply (-4.5 + x) * (3.3 + x) (-4.5(3.3 + x) + x(3.3 + x)) = 0 ((3.3 * -4.5 + x * -4.5) + x(3.3 + x)) = 0 ((-14.85 + -4.5x) + x(3.3 + x)) = 0 (-14.85 + -4.5x + (3.3 * x + x * x)) = 0 (-14.85 + -4.5x + (3.3x + x2)) = 0 Combine like terms: -4.5x + 3.3x = -1.2x (-14.85 + -1.2x + x2) = 0 Solving -14.85 + -1.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '14.85' to each side of the equation. -14.85 + -1.2x + 14.85 + x2 = 0 + 14.85 Reorder the terms: -14.85 + 14.85 + -1.2x + x2 = 0 + 14.85 Combine like terms: -14.85 + 14.85 = 0.00 0.00 + -1.2x + x2 = 0 + 14.85 -1.2x + x2 = 0 + 14.85 Combine like terms: 0 + 14.85 = 14.85 -1.2x + x2 = 14.85 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 14.85 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 14.85 + 0.36 Combine like terms: 14.85 + 0.36 = 15.21 0.36 + -1.2x + x2 = 15.21 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 15.21 Calculate the square root of the right side: 3.9 Break this problem into two subproblems by setting (x + -0.6) equal to 3.9 and -3.9.Subproblem 1
x + -0.6 = 3.9 Simplifying x + -0.6 = 3.9 Reorder the terms: -0.6 + x = 3.9 Solving -0.6 + x = 3.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 3.9 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.9 + 0.6 x = 3.9 + 0.6 Combine like terms: 3.9 + 0.6 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -0.6 = -3.9 Simplifying x + -0.6 = -3.9 Reorder the terms: -0.6 + x = -3.9 Solving -0.6 + x = -3.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -3.9 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.9 + 0.6 x = -3.9 + 0.6 Combine like terms: -3.9 + 0.6 = -3.3 x = -3.3 Simplifying x = -3.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, -3.3}
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