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Simplifying 7x2 + 52x + 2 = 0 Reorder the terms: 2 + 52x + 7x2 = 0 Solving 2 + 52x + 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'. 0.2857142857 + 7.428571429x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 7.428571429x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 7.428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 7.428571429x + x2 = 0 + -0.2857142857 7.428571429x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 7.428571429x + x2 = -0.2857142857 The x term is 7.428571429x. Take half its coefficient (3.714285715). Square it (13.79591837) and add it to both sides. Add '13.79591837' to each side of the equation. 7.428571429x + 13.79591837 + x2 = -0.2857142857 + 13.79591837 Reorder the terms: 13.79591837 + 7.428571429x + x2 = -0.2857142857 + 13.79591837 Combine like terms: -0.2857142857 + 13.79591837 = 13.5102040843 13.79591837 + 7.428571429x + x2 = 13.5102040843 Factor a perfect square on the left side: (x + 3.714285715)(x + 3.714285715) = 13.5102040843 Calculate the square root of the right side: 3.675622952 Break this problem into two subproblems by setting (x + 3.714285715) equal to 3.675622952 and -3.675622952.Subproblem 1
x + 3.714285715 = 3.675622952 Simplifying x + 3.714285715 = 3.675622952 Reorder the terms: 3.714285715 + x = 3.675622952 Solving 3.714285715 + x = 3.675622952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.714285715' to each side of the equation. 3.714285715 + -3.714285715 + x = 3.675622952 + -3.714285715 Combine like terms: 3.714285715 + -3.714285715 = 0.000000000 0.000000000 + x = 3.675622952 + -3.714285715 x = 3.675622952 + -3.714285715 Combine like terms: 3.675622952 + -3.714285715 = -0.038662763 x = -0.038662763 Simplifying x = -0.038662763Subproblem 2
x + 3.714285715 = -3.675622952 Simplifying x + 3.714285715 = -3.675622952 Reorder the terms: 3.714285715 + x = -3.675622952 Solving 3.714285715 + x = -3.675622952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.714285715' to each side of the equation. 3.714285715 + -3.714285715 + x = -3.675622952 + -3.714285715 Combine like terms: 3.714285715 + -3.714285715 = 0.000000000 0.000000000 + x = -3.675622952 + -3.714285715 x = -3.675622952 + -3.714285715 Combine like terms: -3.675622952 + -3.714285715 = -7.389908667 x = -7.389908667 Simplifying x = -7.389908667Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.038662763, -7.389908667}
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