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Simplifying 4x + (3x + 2)(x + -5) = 0 Reorder the terms: 4x + (2 + 3x)(x + -5) = 0 Reorder the terms: 4x + (2 + 3x)(-5 + x) = 0 Multiply (2 + 3x) * (-5 + x) 4x + (2(-5 + x) + 3x * (-5 + x)) = 0 4x + ((-5 * 2 + x * 2) + 3x * (-5 + x)) = 0 4x + ((-10 + 2x) + 3x * (-5 + x)) = 0 4x + (-10 + 2x + (-5 * 3x + x * 3x)) = 0 4x + (-10 + 2x + (-15x + 3x2)) = 0 Combine like terms: 2x + -15x = -13x 4x + (-10 + -13x + 3x2) = 0 Reorder the terms: -10 + 4x + -13x + 3x2 = 0 Combine like terms: 4x + -13x = -9x -10 + -9x + 3x2 = 0 Solving -10 + -9x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -3x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -3x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -3x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -3x + x2 = 0 + 3.333333333 -3x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -3x + x2 = 3.333333333 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 = 3.333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.333333333 + 2.25 Combine like terms: 3.333333333 + 2.25 = 5.583333333 2.25 + -3x + x2 = 5.583333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5.583333333 Calculate the square root of the right side: 2.362907813 Break this problem into two subproblems by setting (x + -1.5) equal to 2.362907813 and -2.362907813.Subproblem 1
x + -1.5 = 2.362907813 Simplifying x + -1.5 = 2.362907813 Reorder the terms: -1.5 + x = 2.362907813 Solving -1.5 + x = 2.362907813 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 = 2.362907813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.362907813 + 1.5 x = 2.362907813 + 1.5 Combine like terms: 2.362907813 + 1.5 = 3.862907813 x = 3.862907813 Simplifying x = 3.862907813Subproblem 2
x + -1.5 = -2.362907813 Simplifying x + -1.5 = -2.362907813 Reorder the terms: -1.5 + x = -2.362907813 Solving -1.5 + x = -2.362907813 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 = -2.362907813 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.362907813 + 1.5 x = -2.362907813 + 1.5 Combine like terms: -2.362907813 + 1.5 = -0.862907813 x = -0.862907813 Simplifying x = -0.862907813Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.862907813, -0.862907813}
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