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Simplifying 5x(x + -4) + 3x = 120 + -4x Reorder the terms: 5x(-4 + x) + 3x = 120 + -4x (-4 * 5x + x * 5x) + 3x = 120 + -4x (-20x + 5x2) + 3x = 120 + -4x Reorder the terms: -20x + 3x + 5x2 = 120 + -4x Combine like terms: -20x + 3x = -17x -17x + 5x2 = 120 + -4x Solving -17x + 5x2 = 120 + -4x Solving for variable 'x'. Reorder the terms: -120 + -17x + 4x + 5x2 = 120 + -4x + -120 + 4x Combine like terms: -17x + 4x = -13x -120 + -13x + 5x2 = 120 + -4x + -120 + 4x Reorder the terms: -120 + -13x + 5x2 = 120 + -120 + -4x + 4x Combine like terms: 120 + -120 = 0 -120 + -13x + 5x2 = 0 + -4x + 4x -120 + -13x + 5x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -120 + -13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -24 + -2.6x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -2.6x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -2.6x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -2.6x + x2 = 0 + 24 -2.6x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -2.6x + x2 = 24 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 24 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 24 + 1.69 Combine like terms: 24 + 1.69 = 25.69 1.69 + -2.6x + x2 = 25.69 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 25.69 Calculate the square root of the right side: 5.068530359 Break this problem into two subproblems by setting (x + -1.3) equal to 5.068530359 and -5.068530359.Subproblem 1
x + -1.3 = 5.068530359 Simplifying x + -1.3 = 5.068530359 Reorder the terms: -1.3 + x = 5.068530359 Solving -1.3 + x = 5.068530359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 5.068530359 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 5.068530359 + 1.3 x = 5.068530359 + 1.3 Combine like terms: 5.068530359 + 1.3 = 6.368530359 x = 6.368530359 Simplifying x = 6.368530359Subproblem 2
x + -1.3 = -5.068530359 Simplifying x + -1.3 = -5.068530359 Reorder the terms: -1.3 + x = -5.068530359 Solving -1.3 + x = -5.068530359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -5.068530359 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -5.068530359 + 1.3 x = -5.068530359 + 1.3 Combine like terms: -5.068530359 + 1.3 = -3.768530359 x = -3.768530359 Simplifying x = -3.768530359Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.368530359, -3.768530359}
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