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Simplifying 21x2 + -18x + -5 = 0 Reorder the terms: -5 + -18x + 21x2 = 0 Solving -5 + -18x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.2380952381 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.2380952381' to each side of the equation. -0.2380952381 + -0.8571428571x + 0.2380952381 + x2 = 0 + 0.2380952381 Reorder the terms: -0.2380952381 + 0.2380952381 + -0.8571428571x + x2 = 0 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.2380952381 -0.8571428571x + x2 = 0 + 0.2380952381 Combine like terms: 0 + 0.2380952381 = 0.2380952381 -0.8571428571x + x2 = 0.2380952381 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.2380952381 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.2380952381 + 0.1836734694 Combine like terms: 0.2380952381 + 0.1836734694 = 0.4217687075 0.1836734694 + -0.8571428571x + x2 = 0.4217687075 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.4217687075 Calculate the square root of the right side: 0.649437224 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.649437224 and -0.649437224.Subproblem 1
x + -0.4285714286 = 0.649437224 Simplifying x + -0.4285714286 = 0.649437224 Reorder the terms: -0.4285714286 + x = 0.649437224 Solving -0.4285714286 + x = 0.649437224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 0.649437224 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.649437224 + 0.4285714286 x = 0.649437224 + 0.4285714286 Combine like terms: 0.649437224 + 0.4285714286 = 1.0780086526 x = 1.0780086526 Simplifying x = 1.0780086526Subproblem 2
x + -0.4285714286 = -0.649437224 Simplifying x + -0.4285714286 = -0.649437224 Reorder the terms: -0.4285714286 + x = -0.649437224 Solving -0.4285714286 + x = -0.649437224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -0.649437224 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.649437224 + 0.4285714286 x = -0.649437224 + 0.4285714286 Combine like terms: -0.649437224 + 0.4285714286 = -0.2208657954 x = -0.2208657954 Simplifying x = -0.2208657954Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0780086526, -0.2208657954}
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