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Simplifying 7x2 + 6x + -2 = 0 Reorder the terms: -2 + 6x + 7x2 = 0 Solving -2 + 6x + 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 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.8571428571x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.8571428571x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + 0.2857142857 0.8571428571x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.8571428571x + x2 = 0.2857142857 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = 0.2857142857 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 0.2857142857 + 0.1836734694 Combine like terms: 0.2857142857 + 0.1836734694 = 0.4693877551 0.1836734694 + 0.8571428571x + x2 = 0.4693877551 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.4693877551 Calculate the square root of the right side: 0.685118789 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.685118789 and -0.685118789.Subproblem 1
x + 0.4285714286 = 0.685118789 Simplifying x + 0.4285714286 = 0.685118789 Reorder the terms: 0.4285714286 + x = 0.685118789 Solving 0.4285714286 + x = 0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = 0.685118789 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.685118789 + -0.4285714286 x = 0.685118789 + -0.4285714286 Combine like terms: 0.685118789 + -0.4285714286 = 0.2565473604 x = 0.2565473604 Simplifying x = 0.2565473604Subproblem 2
x + 0.4285714286 = -0.685118789 Simplifying x + 0.4285714286 = -0.685118789 Reorder the terms: 0.4285714286 + x = -0.685118789 Solving 0.4285714286 + x = -0.685118789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + x = -0.685118789 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.685118789 + -0.4285714286 x = -0.685118789 + -0.4285714286 Combine like terms: -0.685118789 + -0.4285714286 = -1.1136902176 x = -1.1136902176 Simplifying x = -1.1136902176Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2565473604, -1.1136902176}
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