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Simplifying 21x2 + 26x + -8 = 0 Reorder the terms: -8 + 26x + 21x2 = 0 Solving -8 + 26x + 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'. -0.380952381 + 1.238095238x + x2 = 0 Move the constant term to the right: Add '0.380952381' to each side of the equation. -0.380952381 + 1.238095238x + 0.380952381 + x2 = 0 + 0.380952381 Reorder the terms: -0.380952381 + 0.380952381 + 1.238095238x + x2 = 0 + 0.380952381 Combine like terms: -0.380952381 + 0.380952381 = 0.000000000 0.000000000 + 1.238095238x + x2 = 0 + 0.380952381 1.238095238x + x2 = 0 + 0.380952381 Combine like terms: 0 + 0.380952381 = 0.380952381 1.238095238x + x2 = 0.380952381 The x term is 1.238095238x. Take half its coefficient (0.619047619). Square it (0.3832199546) and add it to both sides. Add '0.3832199546' to each side of the equation. 1.238095238x + 0.3832199546 + x2 = 0.380952381 + 0.3832199546 Reorder the terms: 0.3832199546 + 1.238095238x + x2 = 0.380952381 + 0.3832199546 Combine like terms: 0.380952381 + 0.3832199546 = 0.7641723356 0.3832199546 + 1.238095238x + x2 = 0.7641723356 Factor a perfect square on the left side: (x + 0.619047619)(x + 0.619047619) = 0.7641723356 Calculate the square root of the right side: 0.874169512 Break this problem into two subproblems by setting (x + 0.619047619) equal to 0.874169512 and -0.874169512.Subproblem 1
x + 0.619047619 = 0.874169512 Simplifying x + 0.619047619 = 0.874169512 Reorder the terms: 0.619047619 + x = 0.874169512 Solving 0.619047619 + x = 0.874169512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.619047619' to each side of the equation. 0.619047619 + -0.619047619 + x = 0.874169512 + -0.619047619 Combine like terms: 0.619047619 + -0.619047619 = 0.000000000 0.000000000 + x = 0.874169512 + -0.619047619 x = 0.874169512 + -0.619047619 Combine like terms: 0.874169512 + -0.619047619 = 0.255121893 x = 0.255121893 Simplifying x = 0.255121893Subproblem 2
x + 0.619047619 = -0.874169512 Simplifying x + 0.619047619 = -0.874169512 Reorder the terms: 0.619047619 + x = -0.874169512 Solving 0.619047619 + x = -0.874169512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.619047619' to each side of the equation. 0.619047619 + -0.619047619 + x = -0.874169512 + -0.619047619 Combine like terms: 0.619047619 + -0.619047619 = 0.000000000 0.000000000 + x = -0.874169512 + -0.619047619 x = -0.874169512 + -0.619047619 Combine like terms: -0.874169512 + -0.619047619 = -1.493217131 x = -1.493217131 Simplifying x = -1.493217131Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.255121893, -1.493217131}
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