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Simplifying 7x2 + 16x + -21 = 0 Reorder the terms: -21 + 16x + 7x2 = 0 Solving -21 + 16x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.285714286x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.285714286x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.285714286x + x2 = 0 + 3 2.285714286x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.285714286x + x2 = 3 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = 3 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 3 + 1.306122449 Combine like terms: 3 + 1.306122449 = 4.306122449 1.306122449 + 2.285714286x + x2 = 4.306122449 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 4.306122449 Calculate the square root of the right side: 2.075119864 Break this problem into two subproblems by setting (x + 1.142857143) equal to 2.075119864 and -2.075119864.Subproblem 1
x + 1.142857143 = 2.075119864 Simplifying x + 1.142857143 = 2.075119864 Reorder the terms: 1.142857143 + x = 2.075119864 Solving 1.142857143 + x = 2.075119864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = 2.075119864 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 2.075119864 + -1.142857143 x = 2.075119864 + -1.142857143 Combine like terms: 2.075119864 + -1.142857143 = 0.932262721 x = 0.932262721 Simplifying x = 0.932262721Subproblem 2
x + 1.142857143 = -2.075119864 Simplifying x + 1.142857143 = -2.075119864 Reorder the terms: 1.142857143 + x = -2.075119864 Solving 1.142857143 + x = -2.075119864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = -2.075119864 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -2.075119864 + -1.142857143 x = -2.075119864 + -1.142857143 Combine like terms: -2.075119864 + -1.142857143 = -3.217977007 x = -3.217977007 Simplifying x = -3.217977007Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932262721, -3.217977007}
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