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Simplifying 7x2 + -16x + -25 = 0 Reorder the terms: -25 + -16x + 7x2 = 0 Solving -25 + -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'. -3.571428571 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -2.285714286x + 3.571428571 + x2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -2.285714286x + x2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -2.285714286x + x2 = 0 + 3.571428571 -2.285714286x + x2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -2.285714286x + x2 = 3.571428571 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 = 3.571428571 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 3.571428571 + 1.306122449 Combine like terms: 3.571428571 + 1.306122449 = 4.87755102 1.306122449 + -2.285714286x + x2 = 4.87755102 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 4.87755102 Calculate the square root of the right side: 2.208517833 Break this problem into two subproblems by setting (x + -1.142857143) equal to 2.208517833 and -2.208517833.Subproblem 1
x + -1.142857143 = 2.208517833 Simplifying x + -1.142857143 = 2.208517833 Reorder the terms: -1.142857143 + x = 2.208517833 Solving -1.142857143 + x = 2.208517833 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 = 2.208517833 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 2.208517833 + 1.142857143 x = 2.208517833 + 1.142857143 Combine like terms: 2.208517833 + 1.142857143 = 3.351374976 x = 3.351374976 Simplifying x = 3.351374976Subproblem 2
x + -1.142857143 = -2.208517833 Simplifying x + -1.142857143 = -2.208517833 Reorder the terms: -1.142857143 + x = -2.208517833 Solving -1.142857143 + x = -2.208517833 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 = -2.208517833 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -2.208517833 + 1.142857143 x = -2.208517833 + 1.142857143 Combine like terms: -2.208517833 + 1.142857143 = -1.06566069 x = -1.06566069 Simplifying x = -1.06566069Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.351374976, -1.06566069}
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