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Simplifying 7x2 + -16x = 18 Reorder the terms: -16x + 7x2 = 18 Solving -16x + 7x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -16x + 7x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -2.285714286x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -2.285714286x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -2.285714286x + x2 = 0 + 2.571428571 -2.285714286x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -2.285714286x + x2 = 2.571428571 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 = 2.571428571 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 2.571428571 + 1.306122449 Combine like terms: 2.571428571 + 1.306122449 = 3.87755102 1.306122449 + -2.285714286x + x2 = 3.87755102 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 3.87755102 Calculate the square root of the right side: 1.969149822 Break this problem into two subproblems by setting (x + -1.142857143) equal to 1.969149822 and -1.969149822.Subproblem 1
x + -1.142857143 = 1.969149822 Simplifying x + -1.142857143 = 1.969149822 Reorder the terms: -1.142857143 + x = 1.969149822 Solving -1.142857143 + x = 1.969149822 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 = 1.969149822 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.969149822 + 1.142857143 x = 1.969149822 + 1.142857143 Combine like terms: 1.969149822 + 1.142857143 = 3.112006965 x = 3.112006965 Simplifying x = 3.112006965Subproblem 2
x + -1.142857143 = -1.969149822 Simplifying x + -1.142857143 = -1.969149822 Reorder the terms: -1.142857143 + x = -1.969149822 Solving -1.142857143 + x = -1.969149822 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 = -1.969149822 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.969149822 + 1.142857143 x = -1.969149822 + 1.142857143 Combine like terms: -1.969149822 + 1.142857143 = -0.826292679 x = -0.826292679 Simplifying x = -0.826292679Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.112006965, -0.826292679}
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