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Simplifying 2(4x + -9) = 5x(x + -4) Reorder the terms: 2(-9 + 4x) = 5x(x + -4) (-9 * 2 + 4x * 2) = 5x(x + -4) (-18 + 8x) = 5x(x + -4) Reorder the terms: -18 + 8x = 5x(-4 + x) -18 + 8x = (-4 * 5x + x * 5x) -18 + 8x = (-20x + 5x2) Solving -18 + 8x = -20x + 5x2 Solving for variable 'x'. Combine like terms: 8x + 20x = 28x -18 + 28x + -5x2 = -20x + 5x2 + 20x + -5x2 Reorder the terms: -18 + 28x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -18 + 28x + -5x2 = 0 + 5x2 + -5x2 -18 + 28x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -18 + 28x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.6 + -5.6x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -5.6x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -5.6x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -5.6x + x2 = 0 + -3.6 -5.6x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -5.6x + x2 = -3.6 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = -3.6 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = -3.6 + 7.84 Combine like terms: -3.6 + 7.84 = 4.24 7.84 + -5.6x + x2 = 4.24 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + -2.8) equal to 2.059126028 and -2.059126028.Subproblem 1
x + -2.8 = 2.059126028 Simplifying x + -2.8 = 2.059126028 Reorder the terms: -2.8 + x = 2.059126028 Solving -2.8 + x = 2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 2.059126028 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 2.059126028 + 2.8 x = 2.059126028 + 2.8 Combine like terms: 2.059126028 + 2.8 = 4.859126028 x = 4.859126028 Simplifying x = 4.859126028Subproblem 2
x + -2.8 = -2.059126028 Simplifying x + -2.8 = -2.059126028 Reorder the terms: -2.8 + x = -2.059126028 Solving -2.8 + x = -2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -2.059126028 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -2.059126028 + 2.8 x = -2.059126028 + 2.8 Combine like terms: -2.059126028 + 2.8 = 0.740873972 x = 0.740873972 Simplifying x = 0.740873972Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.859126028, 0.740873972}
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