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Simplifying (0.25 + 7x)(0.05 + -8x) = 0 Multiply (0.25 + 7x) * (0.05 + -8x) (0.25(0.05 + -8x) + 7x * (0.05 + -8x)) = 0 ((0.05 * 0.25 + -8x * 0.25) + 7x * (0.05 + -8x)) = 0 ((0.0125 + -2x) + 7x * (0.05 + -8x)) = 0 (0.0125 + -2x + (0.05 * 7x + -8x * 7x)) = 0 (0.0125 + -2x + (0.35x + -56x2)) = 0 Combine like terms: -2x + 0.35x = -1.65x (0.0125 + -1.65x + -56x2) = 0 Solving 0.0125 + -1.65x + -56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -56 the coefficient of the squared term: Divide each side by '-56'. -0.0002232142857 + 0.02946428571x + x2 = 0 Move the constant term to the right: Add '0.0002232142857' to each side of the equation. -0.0002232142857 + 0.02946428571x + 0.0002232142857 + x2 = 0 + 0.0002232142857 Reorder the terms: -0.0002232142857 + 0.0002232142857 + 0.02946428571x + x2 = 0 + 0.0002232142857 Combine like terms: -0.0002232142857 + 0.0002232142857 = 0.0000000000000 0.0000000000000 + 0.02946428571x + x2 = 0 + 0.0002232142857 0.02946428571x + x2 = 0 + 0.0002232142857 Combine like terms: 0 + 0.0002232142857 = 0.0002232142857 0.02946428571x + x2 = 0.0002232142857 The x term is 0.02946428571x. Take half its coefficient (0.01473214286). Square it (0.0002170360332) and add it to both sides. Add '0.0002170360332' to each side of the equation. 0.02946428571x + 0.0002170360332 + x2 = 0.0002232142857 + 0.0002170360332 Reorder the terms: 0.0002170360332 + 0.02946428571x + x2 = 0.0002232142857 + 0.0002170360332 Combine like terms: 0.0002232142857 + 0.0002170360332 = 0.0004402503189 0.0002170360332 + 0.02946428571x + x2 = 0.0004402503189 Factor a perfect square on the left side: (x + 0.01473214286)(x + 0.01473214286) = 0.0004402503189 Calculate the square root of the right side: 0.020982143 Break this problem into two subproblems by setting (x + 0.01473214286) equal to 0.020982143 and -0.020982143.Subproblem 1
x + 0.01473214286 = 0.020982143 Simplifying x + 0.01473214286 = 0.020982143 Reorder the terms: 0.01473214286 + x = 0.020982143 Solving 0.01473214286 + x = 0.020982143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01473214286' to each side of the equation. 0.01473214286 + -0.01473214286 + x = 0.020982143 + -0.01473214286 Combine like terms: 0.01473214286 + -0.01473214286 = 0.00000000000 0.00000000000 + x = 0.020982143 + -0.01473214286 x = 0.020982143 + -0.01473214286 Combine like terms: 0.020982143 + -0.01473214286 = 0.00625000014 x = 0.00625000014 Simplifying x = 0.00625000014Subproblem 2
x + 0.01473214286 = -0.020982143 Simplifying x + 0.01473214286 = -0.020982143 Reorder the terms: 0.01473214286 + x = -0.020982143 Solving 0.01473214286 + x = -0.020982143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01473214286' to each side of the equation. 0.01473214286 + -0.01473214286 + x = -0.020982143 + -0.01473214286 Combine like terms: 0.01473214286 + -0.01473214286 = 0.00000000000 0.00000000000 + x = -0.020982143 + -0.01473214286 x = -0.020982143 + -0.01473214286 Combine like terms: -0.020982143 + -0.01473214286 = -0.03571428586 x = -0.03571428586 Simplifying x = -0.03571428586Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00625000014, -0.03571428586}
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