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Simplifying 5x(x + -4) + -4(x + -5) = 0 Reorder the terms: 5x(-4 + x) + -4(x + -5) = 0 (-4 * 5x + x * 5x) + -4(x + -5) = 0 (-20x + 5x2) + -4(x + -5) = 0 Reorder the terms: -20x + 5x2 + -4(-5 + x) = 0 -20x + 5x2 + (-5 * -4 + x * -4) = 0 -20x + 5x2 + (20 + -4x) = 0 Reorder the terms: 20 + -20x + -4x + 5x2 = 0 Combine like terms: -20x + -4x = -24x 20 + -24x + 5x2 = 0 Solving 20 + -24x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -4.8x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.8x + x2 = 0 + -4 -4.8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.8x + x2 = -4 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = -4 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -4 + 5.76 Combine like terms: -4 + 5.76 = 1.76 5.76 + -4.8x + x2 = 1.76 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -2.4) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -2.4 = 1.326649916 Simplifying x + -2.4 = 1.326649916 Reorder the terms: -2.4 + x = 1.326649916 Solving -2.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 1.326649916 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 1.326649916 + 2.4 x = 1.326649916 + 2.4 Combine like terms: 1.326649916 + 2.4 = 3.726649916 x = 3.726649916 Simplifying x = 3.726649916Subproblem 2
x + -2.4 = -1.326649916 Simplifying x + -2.4 = -1.326649916 Reorder the terms: -2.4 + x = -1.326649916 Solving -2.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -1.326649916 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -1.326649916 + 2.4 x = -1.326649916 + 2.4 Combine like terms: -1.326649916 + 2.4 = 1.073350084 x = 1.073350084 Simplifying x = 1.073350084Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.726649916, 1.073350084}
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