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Simplifying 7x2 + -16x = 8 Reorder the terms: -16x + 7x2 = 8 Solving -16x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -16x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -2.285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -2.285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -2.285714286x + x2 = 0 + 1.142857143 -2.285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -2.285714286x + x2 = 1.142857143 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 = 1.142857143 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 1.142857143 + 1.306122449 Combine like terms: 1.142857143 + 1.306122449 = 2.448979592 1.306122449 + -2.285714286x + x2 = 2.448979592 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 2.448979592 Calculate the square root of the right side: 1.564921593 Break this problem into two subproblems by setting (x + -1.142857143) equal to 1.564921593 and -1.564921593.Subproblem 1
x + -1.142857143 = 1.564921593 Simplifying x + -1.142857143 = 1.564921593 Reorder the terms: -1.142857143 + x = 1.564921593 Solving -1.142857143 + x = 1.564921593 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 = 1.564921593 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.564921593 + 1.142857143 x = 1.564921593 + 1.142857143 Combine like terms: 1.564921593 + 1.142857143 = 2.707778736 x = 2.707778736 Simplifying x = 2.707778736Subproblem 2
x + -1.142857143 = -1.564921593 Simplifying x + -1.142857143 = -1.564921593 Reorder the terms: -1.142857143 + x = -1.564921593 Solving -1.142857143 + x = -1.564921593 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 = -1.564921593 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.564921593 + 1.142857143 x = -1.564921593 + 1.142857143 Combine like terms: -1.564921593 + 1.142857143 = -0.42206445 x = -0.42206445 Simplifying x = -0.42206445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.707778736, -0.42206445}
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