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Simplifying (6.4 + x)(5.6 + x) = 0 Multiply (6.4 + x) * (5.6 + x) (6.4(5.6 + x) + x(5.6 + x)) = 0 ((5.6 * 6.4 + x * 6.4) + x(5.6 + x)) = 0 ((35.84 + 6.4x) + x(5.6 + x)) = 0 (35.84 + 6.4x + (5.6 * x + x * x)) = 0 (35.84 + 6.4x + (5.6x + x2)) = 0 Combine like terms: 6.4x + 5.6x = 12x (35.84 + 12x + x2) = 0 Solving 35.84 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35.84' to each side of the equation. 35.84 + 12x + -35.84 + x2 = 0 + -35.84 Reorder the terms: 35.84 + -35.84 + 12x + x2 = 0 + -35.84 Combine like terms: 35.84 + -35.84 = 0.00 0.00 + 12x + x2 = 0 + -35.84 12x + x2 = 0 + -35.84 Combine like terms: 0 + -35.84 = -35.84 12x + x2 = -35.84 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -35.84 + 36 Reorder the terms: 36 + 12x + x2 = -35.84 + 36 Combine like terms: -35.84 + 36 = 0.16 36 + 12x + x2 = 0.16 Factor a perfect square on the left side: (x + 6)(x + 6) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + 6) equal to 0.4 and -0.4.Subproblem 1
x + 6 = 0.4 Simplifying x + 6 = 0.4 Reorder the terms: 6 + x = 0.4 Solving 6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0.4 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0.4 + -6 x = 0.4 + -6 Combine like terms: 0.4 + -6 = -5.6 x = -5.6 Simplifying x = -5.6Subproblem 2
x + 6 = -0.4 Simplifying x + 6 = -0.4 Reorder the terms: 6 + x = -0.4 Solving 6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -0.4 + -6 Combine like terms: 6 + -6 = 0 0 + x = -0.4 + -6 x = -0.4 + -6 Combine like terms: -0.4 + -6 = -6.4 x = -6.4 Simplifying x = -6.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.6, -6.4}
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