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Simplifying 9 + -16x + -7x2 = 0 Solving 9 + -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'. -1.285714286 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 2.285714286x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 2.285714286x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + 1.285714286 2.285714286x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 2.285714286x + x2 = 1.285714286 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 = 1.285714286 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 1.285714286 + 1.306122449 Combine like terms: 1.285714286 + 1.306122449 = 2.591836735 1.306122449 + 2.285714286x + x2 = 2.591836735 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 2.591836735 Calculate the square root of the right side: 1.609918239 Break this problem into two subproblems by setting (x + 1.142857143) equal to 1.609918239 and -1.609918239.Subproblem 1
x + 1.142857143 = 1.609918239 Simplifying x + 1.142857143 = 1.609918239 Reorder the terms: 1.142857143 + x = 1.609918239 Solving 1.142857143 + x = 1.609918239 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 = 1.609918239 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 1.609918239 + -1.142857143 x = 1.609918239 + -1.142857143 Combine like terms: 1.609918239 + -1.142857143 = 0.467061096 x = 0.467061096 Simplifying x = 0.467061096Subproblem 2
x + 1.142857143 = -1.609918239 Simplifying x + 1.142857143 = -1.609918239 Reorder the terms: 1.142857143 + x = -1.609918239 Solving 1.142857143 + x = -1.609918239 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 = -1.609918239 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -1.609918239 + -1.142857143 x = -1.609918239 + -1.142857143 Combine like terms: -1.609918239 + -1.142857143 = -2.752775382 x = -2.752775382 Simplifying x = -2.752775382Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.467061096, -2.752775382}
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