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Simplifying 6x2 + -5x + -21 = 20 Reorder the terms: -21 + -5x + 6x2 = 20 Solving -21 + -5x + 6x2 = 20 Solving for variable 'x'. Reorder the terms: -21 + -20 + -5x + 6x2 = 20 + -20 Combine like terms: -21 + -20 = -41 -41 + -5x + 6x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -41 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.833333333 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '6.833333333' to each side of the equation. -6.833333333 + -0.8333333333x + 6.833333333 + x2 = 0 + 6.833333333 Reorder the terms: -6.833333333 + 6.833333333 + -0.8333333333x + x2 = 0 + 6.833333333 Combine like terms: -6.833333333 + 6.833333333 = 0.000000000 0.000000000 + -0.8333333333x + x2 = 0 + 6.833333333 -0.8333333333x + x2 = 0 + 6.833333333 Combine like terms: 0 + 6.833333333 = 6.833333333 -0.8333333333x + x2 = 6.833333333 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 6.833333333 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 6.833333333 + 0.1736111111 Combine like terms: 6.833333333 + 0.1736111111 = 7.0069444441 0.1736111111 + -0.8333333333x + x2 = 7.0069444441 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 7.0069444441 Calculate the square root of the right side: 2.647063362 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 2.647063362 and -2.647063362.Subproblem 1
x + -0.4166666667 = 2.647063362 Simplifying x + -0.4166666667 = 2.647063362 Reorder the terms: -0.4166666667 + x = 2.647063362 Solving -0.4166666667 + x = 2.647063362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 2.647063362 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 2.647063362 + 0.4166666667 x = 2.647063362 + 0.4166666667 Combine like terms: 2.647063362 + 0.4166666667 = 3.0637300287 x = 3.0637300287 Simplifying x = 3.0637300287Subproblem 2
x + -0.4166666667 = -2.647063362 Simplifying x + -0.4166666667 = -2.647063362 Reorder the terms: -0.4166666667 + x = -2.647063362 Solving -0.4166666667 + x = -2.647063362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -2.647063362 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -2.647063362 + 0.4166666667 x = -2.647063362 + 0.4166666667 Combine like terms: -2.647063362 + 0.4166666667 = -2.2303966953 x = -2.2303966953 Simplifying x = -2.2303966953Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.0637300287, -2.2303966953}
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