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Simplifying (4x + -1.6)(8 + x) = 0 Reorder the terms: (-1.6 + 4x)(8 + x) = 0 Multiply (-1.6 + 4x) * (8 + x) (-1.6(8 + x) + 4x * (8 + x)) = 0 ((8 * -1.6 + x * -1.6) + 4x * (8 + x)) = 0 ((-12.8 + -1.6x) + 4x * (8 + x)) = 0 (-12.8 + -1.6x + (8 * 4x + x * 4x)) = 0 (-12.8 + -1.6x + (32x + 4x2)) = 0 Combine like terms: -1.6x + 32x = 30.4x (-12.8 + 30.4x + 4x2) = 0 Solving -12.8 + 30.4x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.2 + 7.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 7.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 7.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 7.6x + x2 = 0 + 3.2 7.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 7.6x + x2 = 3.2 The x term is 7.6x. Take half its coefficient (3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. 7.6x + 14.44 + x2 = 3.2 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = 3.2 + 14.44 Combine like terms: 3.2 + 14.44 = 17.64 14.44 + 7.6x + x2 = 17.64 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 17.64 Calculate the square root of the right side: 4.2 Break this problem into two subproblems by setting (x + 3.8) equal to 4.2 and -4.2.Subproblem 1
x + 3.8 = 4.2 Simplifying x + 3.8 = 4.2 Reorder the terms: 3.8 + x = 4.2 Solving 3.8 + x = 4.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = 4.2 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 4.2 + -3.8 x = 4.2 + -3.8 Combine like terms: 4.2 + -3.8 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 3.8 = -4.2 Simplifying x + 3.8 = -4.2 Reorder the terms: 3.8 + x = -4.2 Solving 3.8 + x = -4.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = -4.2 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -4.2 + -3.8 x = -4.2 + -3.8 Combine like terms: -4.2 + -3.8 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -8}
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