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Simplifying 21x2 + -69x + 20 = 0 Reorder the terms: 20 + -69x + 21x2 = 0 Solving 20 + -69x + 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'. 0.9523809524 + -3.285714286x + x2 = 0 Move the constant term to the right: Add '-0.9523809524' to each side of the equation. 0.9523809524 + -3.285714286x + -0.9523809524 + x2 = 0 + -0.9523809524 Reorder the terms: 0.9523809524 + -0.9523809524 + -3.285714286x + x2 = 0 + -0.9523809524 Combine like terms: 0.9523809524 + -0.9523809524 = 0.0000000000 0.0000000000 + -3.285714286x + x2 = 0 + -0.9523809524 -3.285714286x + x2 = 0 + -0.9523809524 Combine like terms: 0 + -0.9523809524 = -0.9523809524 -3.285714286x + x2 = -0.9523809524 The x term is -3.285714286x. Take half its coefficient (-1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. -3.285714286x + 2.698979592 + x2 = -0.9523809524 + 2.698979592 Reorder the terms: 2.698979592 + -3.285714286x + x2 = -0.9523809524 + 2.698979592 Combine like terms: -0.9523809524 + 2.698979592 = 1.7465986396 2.698979592 + -3.285714286x + x2 = 1.7465986396 Factor a perfect square on the left side: (x + -1.642857143)(x + -1.642857143) = 1.7465986396 Calculate the square root of the right side: 1.321589437 Break this problem into two subproblems by setting (x + -1.642857143) equal to 1.321589437 and -1.321589437.Subproblem 1
x + -1.642857143 = 1.321589437 Simplifying x + -1.642857143 = 1.321589437 Reorder the terms: -1.642857143 + x = 1.321589437 Solving -1.642857143 + x = 1.321589437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = 1.321589437 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 1.321589437 + 1.642857143 x = 1.321589437 + 1.642857143 Combine like terms: 1.321589437 + 1.642857143 = 2.96444658 x = 2.96444658 Simplifying x = 2.96444658Subproblem 2
x + -1.642857143 = -1.321589437 Simplifying x + -1.642857143 = -1.321589437 Reorder the terms: -1.642857143 + x = -1.321589437 Solving -1.642857143 + x = -1.321589437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = -1.321589437 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -1.321589437 + 1.642857143 x = -1.321589437 + 1.642857143 Combine like terms: -1.321589437 + 1.642857143 = 0.321267706 x = 0.321267706 Simplifying x = 0.321267706Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.96444658, 0.321267706}
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