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Simplifying 28x2 + -1x + -12 = 0 Reorder the terms: -12 + -1x + 28x2 = 0 Solving -12 + -1x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.4285714286 + -0.03571428571x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.03571428571x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.03571428571x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.03571428571x + x2 = 0 + 0.4285714286 -0.03571428571x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.03571428571x + x2 = 0.4285714286 The x term is -0.03571428571x. Take half its coefficient (-0.01785714286). Square it (0.0003188775511) and add it to both sides. Add '0.0003188775511' to each side of the equation. -0.03571428571x + 0.0003188775511 + x2 = 0.4285714286 + 0.0003188775511 Reorder the terms: 0.0003188775511 + -0.03571428571x + x2 = 0.4285714286 + 0.0003188775511 Combine like terms: 0.4285714286 + 0.0003188775511 = 0.4288903061511 0.0003188775511 + -0.03571428571x + x2 = 0.4288903061511 Factor a perfect square on the left side: (x + -0.01785714286)(x + -0.01785714286) = 0.4288903061511 Calculate the square root of the right side: 0.654897172 Break this problem into two subproblems by setting (x + -0.01785714286) equal to 0.654897172 and -0.654897172.Subproblem 1
x + -0.01785714286 = 0.654897172 Simplifying x + -0.01785714286 = 0.654897172 Reorder the terms: -0.01785714286 + x = 0.654897172 Solving -0.01785714286 + x = 0.654897172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01785714286' to each side of the equation. -0.01785714286 + 0.01785714286 + x = 0.654897172 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + x = 0.654897172 + 0.01785714286 x = 0.654897172 + 0.01785714286 Combine like terms: 0.654897172 + 0.01785714286 = 0.67275431486 x = 0.67275431486 Simplifying x = 0.67275431486Subproblem 2
x + -0.01785714286 = -0.654897172 Simplifying x + -0.01785714286 = -0.654897172 Reorder the terms: -0.01785714286 + x = -0.654897172 Solving -0.01785714286 + x = -0.654897172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01785714286' to each side of the equation. -0.01785714286 + 0.01785714286 + x = -0.654897172 + 0.01785714286 Combine like terms: -0.01785714286 + 0.01785714286 = 0.00000000000 0.00000000000 + x = -0.654897172 + 0.01785714286 x = -0.654897172 + 0.01785714286 Combine like terms: -0.654897172 + 0.01785714286 = -0.63704002914 x = -0.63704002914 Simplifying x = -0.63704002914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67275431486, -0.63704002914}
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