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Simplifying 3x + -8 = 5x(x + -4) Reorder the terms: -8 + 3x = 5x(x + -4) Reorder the terms: -8 + 3x = 5x(-4 + x) -8 + 3x = (-4 * 5x + x * 5x) -8 + 3x = (-20x + 5x2) Solving -8 + 3x = -20x + 5x2 Solving for variable 'x'. Combine like terms: 3x + 20x = 23x -8 + 23x + -5x2 = -20x + 5x2 + 20x + -5x2 Reorder the terms: -8 + 23x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -8 + 23x + -5x2 = 0 + 5x2 + -5x2 -8 + 23x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8 + 23x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.6 + -4.6x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -4.6x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -4.6x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -4.6x + x2 = 0 + -1.6 -4.6x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -4.6x + x2 = -1.6 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = -1.6 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = -1.6 + 5.29 Combine like terms: -1.6 + 5.29 = 3.69 5.29 + -4.6x + x2 = 3.69 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (x + -2.3) equal to 1.920937271 and -1.920937271.Subproblem 1
x + -2.3 = 1.920937271 Simplifying x + -2.3 = 1.920937271 Reorder the terms: -2.3 + x = 1.920937271 Solving -2.3 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 1.920937271 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 1.920937271 + 2.3 x = 1.920937271 + 2.3 Combine like terms: 1.920937271 + 2.3 = 4.220937271 x = 4.220937271 Simplifying x = 4.220937271Subproblem 2
x + -2.3 = -1.920937271 Simplifying x + -2.3 = -1.920937271 Reorder the terms: -2.3 + x = -1.920937271 Solving -2.3 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -1.920937271 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -1.920937271 + 2.3 x = -1.920937271 + 2.3 Combine like terms: -1.920937271 + 2.3 = 0.379062729 x = 0.379062729 Simplifying x = 0.379062729Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.220937271, 0.379062729}
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