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Simplifying 7x2 + -16x + -28 = 0 Reorder the terms: -28 + -16x + 7x2 = 0 Solving -28 + -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'. -4 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.285714286x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.285714286x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.285714286x + x2 = 0 + 4 -2.285714286x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.285714286x + x2 = 4 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 = 4 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 4 + 1.306122449 Combine like terms: 4 + 1.306122449 = 5.306122449 1.306122449 + -2.285714286x + x2 = 5.306122449 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 5.306122449 Calculate the square root of the right side: 2.303502214 Break this problem into two subproblems by setting (x + -1.142857143) equal to 2.303502214 and -2.303502214.Subproblem 1
x + -1.142857143 = 2.303502214 Simplifying x + -1.142857143 = 2.303502214 Reorder the terms: -1.142857143 + x = 2.303502214 Solving -1.142857143 + x = 2.303502214 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 = 2.303502214 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 2.303502214 + 1.142857143 x = 2.303502214 + 1.142857143 Combine like terms: 2.303502214 + 1.142857143 = 3.446359357 x = 3.446359357 Simplifying x = 3.446359357Subproblem 2
x + -1.142857143 = -2.303502214 Simplifying x + -1.142857143 = -2.303502214 Reorder the terms: -1.142857143 + x = -2.303502214 Solving -1.142857143 + x = -2.303502214 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 = -2.303502214 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -2.303502214 + 1.142857143 x = -2.303502214 + 1.142857143 Combine like terms: -2.303502214 + 1.142857143 = -1.160645071 x = -1.160645071 Simplifying x = -1.160645071Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.446359357, -1.160645071}
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