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Simplifying (x + 4)(5x + -1) = 16 Reorder the terms: (4 + x)(5x + -1) = 16 Reorder the terms: (4 + x)(-1 + 5x) = 16 Multiply (4 + x) * (-1 + 5x) (4(-1 + 5x) + x(-1 + 5x)) = 16 ((-1 * 4 + 5x * 4) + x(-1 + 5x)) = 16 ((-4 + 20x) + x(-1 + 5x)) = 16 (-4 + 20x + (-1 * x + 5x * x)) = 16 (-4 + 20x + (-1x + 5x2)) = 16 Combine like terms: 20x + -1x = 19x (-4 + 19x + 5x2) = 16 Solving -4 + 19x + 5x2 = 16 Solving for variable 'x'. Reorder the terms: -4 + -16 + 19x + 5x2 = 16 + -16 Combine like terms: -4 + -16 = -20 -20 + 19x + 5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -20 + 19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 3.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 3.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 3.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3.8x + x2 = 0 + 4 3.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 3.8x + x2 = 4 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 4 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 4 + 3.61 Combine like terms: 4 + 3.61 = 7.61 3.61 + 3.8x + x2 = 7.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 7.61 Calculate the square root of the right side: 2.758622845 Break this problem into two subproblems by setting (x + 1.9) equal to 2.758622845 and -2.758622845.Subproblem 1
x + 1.9 = 2.758622845 Simplifying x + 1.9 = 2.758622845 Reorder the terms: 1.9 + x = 2.758622845 Solving 1.9 + x = 2.758622845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 2.758622845 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 2.758622845 + -1.9 x = 2.758622845 + -1.9 Combine like terms: 2.758622845 + -1.9 = 0.858622845 x = 0.858622845 Simplifying x = 0.858622845Subproblem 2
x + 1.9 = -2.758622845 Simplifying x + 1.9 = -2.758622845 Reorder the terms: 1.9 + x = -2.758622845 Solving 1.9 + x = -2.758622845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -2.758622845 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -2.758622845 + -1.9 x = -2.758622845 + -1.9 Combine like terms: -2.758622845 + -1.9 = -4.658622845 x = -4.658622845 Simplifying x = -4.658622845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.858622845, -4.658622845}
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