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Simplifying 6x2 + 7x + -21 = 0 Reorder the terms: -21 + 7x + 6x2 = 0 Solving -21 + 7x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.5 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 1.166666667x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 1.166666667x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 1.166666667x + x2 = 0 + 3.5 1.166666667x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 1.166666667x + x2 = 3.5 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 3.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 3.5 + 0.3402777780 Combine like terms: 3.5 + 0.3402777780 = 3.840277778 0.3402777780 + 1.166666667x + x2 = 3.840277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 3.840277778 Calculate the square root of the right side: 1.959662669 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.959662669 and -1.959662669.Subproblem 1
x + 0.5833333335 = 1.959662669 Simplifying x + 0.5833333335 = 1.959662669 Reorder the terms: 0.5833333335 + x = 1.959662669 Solving 0.5833333335 + x = 1.959662669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 1.959662669 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.959662669 + -0.5833333335 x = 1.959662669 + -0.5833333335 Combine like terms: 1.959662669 + -0.5833333335 = 1.3763293355 x = 1.3763293355 Simplifying x = 1.3763293355Subproblem 2
x + 0.5833333335 = -1.959662669 Simplifying x + 0.5833333335 = -1.959662669 Reorder the terms: 0.5833333335 + x = -1.959662669 Solving 0.5833333335 + x = -1.959662669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -1.959662669 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.959662669 + -0.5833333335 x = -1.959662669 + -0.5833333335 Combine like terms: -1.959662669 + -0.5833333335 = -2.5429960025 x = -2.5429960025 Simplifying x = -2.5429960025Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3763293355, -2.5429960025}
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