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Simplifying 7x2 + 22x = -14 Reorder the terms: 22x + 7x2 = -14 Solving 22x + 7x2 = -14 Solving for variable 'x'. Reorder the terms: 14 + 22x + 7x2 = -14 + 14 Combine like terms: -14 + 14 = 0 14 + 22x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.142857143x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.142857143x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.142857143x + x2 = 0 + -2 3.142857143x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.142857143x + x2 = -2 The x term is 3.142857143x. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143x + 2.469387757 + x2 = -2 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = -2 + 2.469387757 Combine like terms: -2 + 2.469387757 = 0.469387757 2.469387757 + 3.142857143x + x2 = 0.469387757 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 0.469387757 Calculate the square root of the right side: 0.68511879 Break this problem into two subproblems by setting (x + 1.571428572) equal to 0.68511879 and -0.68511879.Subproblem 1
x + 1.571428572 = 0.68511879 Simplifying x + 1.571428572 = 0.68511879 Reorder the terms: 1.571428572 + x = 0.68511879 Solving 1.571428572 + x = 0.68511879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 0.68511879 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 0.68511879 + -1.571428572 x = 0.68511879 + -1.571428572 Combine like terms: 0.68511879 + -1.571428572 = -0.886309782 x = -0.886309782 Simplifying x = -0.886309782Subproblem 2
x + 1.571428572 = -0.68511879 Simplifying x + 1.571428572 = -0.68511879 Reorder the terms: 1.571428572 + x = -0.68511879 Solving 1.571428572 + x = -0.68511879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -0.68511879 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -0.68511879 + -1.571428572 x = -0.68511879 + -1.571428572 Combine like terms: -0.68511879 + -1.571428572 = -2.256547362 x = -2.256547362 Simplifying x = -2.256547362Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.886309782, -2.256547362}
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