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Simplifying 21x * x + 25x + -294 = 0 Multiply x * x 21x2 + 25x + -294 = 0 Reorder the terms: -294 + 25x + 21x2 = 0 Solving -294 + 25x + 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'. -14 + 1.19047619x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 1.19047619x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 1.19047619x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 1.19047619x + x2 = 0 + 14 1.19047619x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 1.19047619x + x2 = 14 The x term is 1.19047619x. Take half its coefficient (0.595238095). Square it (0.3543083897) and add it to both sides. Add '0.3543083897' to each side of the equation. 1.19047619x + 0.3543083897 + x2 = 14 + 0.3543083897 Reorder the terms: 0.3543083897 + 1.19047619x + x2 = 14 + 0.3543083897 Combine like terms: 14 + 0.3543083897 = 14.3543083897 0.3543083897 + 1.19047619x + x2 = 14.3543083897 Factor a perfect square on the left side: (x + 0.595238095)(x + 0.595238095) = 14.3543083897 Calculate the square root of the right side: 3.788708011 Break this problem into two subproblems by setting (x + 0.595238095) equal to 3.788708011 and -3.788708011.Subproblem 1
x + 0.595238095 = 3.788708011 Simplifying x + 0.595238095 = 3.788708011 Reorder the terms: 0.595238095 + x = 3.788708011 Solving 0.595238095 + x = 3.788708011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.595238095' to each side of the equation. 0.595238095 + -0.595238095 + x = 3.788708011 + -0.595238095 Combine like terms: 0.595238095 + -0.595238095 = 0.000000000 0.000000000 + x = 3.788708011 + -0.595238095 x = 3.788708011 + -0.595238095 Combine like terms: 3.788708011 + -0.595238095 = 3.193469916 x = 3.193469916 Simplifying x = 3.193469916Subproblem 2
x + 0.595238095 = -3.788708011 Simplifying x + 0.595238095 = -3.788708011 Reorder the terms: 0.595238095 + x = -3.788708011 Solving 0.595238095 + x = -3.788708011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.595238095' to each side of the equation. 0.595238095 + -0.595238095 + x = -3.788708011 + -0.595238095 Combine like terms: 0.595238095 + -0.595238095 = 0.000000000 0.000000000 + x = -3.788708011 + -0.595238095 x = -3.788708011 + -0.595238095 Combine like terms: -3.788708011 + -0.595238095 = -4.383946106 x = -4.383946106 Simplifying x = -4.383946106Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.193469916, -4.383946106}
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