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Simplifying 7x2 + -16x + -7 = 0 Reorder the terms: -7 + -16x + 7x2 = 0 Solving -7 + -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'. -1 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.285714286x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.285714286x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.285714286x + x2 = 0 + 1 -2.285714286x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.285714286x + x2 = 1 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 = 1 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 1 + 1.306122449 Combine like terms: 1 + 1.306122449 = 2.306122449 1.306122449 + -2.285714286x + x2 = 2.306122449 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 2.306122449 Calculate the square root of the right side: 1.518592259 Break this problem into two subproblems by setting (x + -1.142857143) equal to 1.518592259 and -1.518592259.Subproblem 1
x + -1.142857143 = 1.518592259 Simplifying x + -1.142857143 = 1.518592259 Reorder the terms: -1.142857143 + x = 1.518592259 Solving -1.142857143 + x = 1.518592259 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 = 1.518592259 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.518592259 + 1.142857143 x = 1.518592259 + 1.142857143 Combine like terms: 1.518592259 + 1.142857143 = 2.661449402 x = 2.661449402 Simplifying x = 2.661449402Subproblem 2
x + -1.142857143 = -1.518592259 Simplifying x + -1.142857143 = -1.518592259 Reorder the terms: -1.142857143 + x = -1.518592259 Solving -1.142857143 + x = -1.518592259 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 = -1.518592259 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.518592259 + 1.142857143 x = -1.518592259 + 1.142857143 Combine like terms: -1.518592259 + 1.142857143 = -0.375735116 x = -0.375735116 Simplifying x = -0.375735116Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.661449402, -0.375735116}
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