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Simplifying 7x2 = 7 + -6x Solving 7x2 = 7 + -6x Solving for variable 'x'. Reorder the terms: -7 + 6x + 7x2 = 7 + -6x + -7 + 6x Reorder the terms: -7 + 6x + 7x2 = 7 + -7 + -6x + 6x Combine like terms: 7 + -7 = 0 -7 + 6x + 7x2 = 0 + -6x + 6x -7 + 6x + 7x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -7 + 6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.8571428571x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.8571428571x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.8571428571x + x2 = 0 + 1 0.8571428571x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.8571428571x + x2 = 1 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 = 1 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 1 + 0.1836734694 Combine like terms: 1 + 0.1836734694 = 1.1836734694 0.1836734694 + 0.8571428571x + x2 = 1.1836734694 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.087967587 and -1.087967587.Subproblem 1
x + 0.4285714286 = 1.087967587 Simplifying x + 0.4285714286 = 1.087967587 Reorder the terms: 0.4285714286 + x = 1.087967587 Solving 0.4285714286 + x = 1.087967587 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 = 1.087967587 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.087967587 + -0.4285714286 x = 1.087967587 + -0.4285714286 Combine like terms: 1.087967587 + -0.4285714286 = 0.6593961584 x = 0.6593961584 Simplifying x = 0.6593961584Subproblem 2
x + 0.4285714286 = -1.087967587 Simplifying x + 0.4285714286 = -1.087967587 Reorder the terms: 0.4285714286 + x = -1.087967587 Solving 0.4285714286 + x = -1.087967587 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 = -1.087967587 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.087967587 + -0.4285714286 x = -1.087967587 + -0.4285714286 Combine like terms: -1.087967587 + -0.4285714286 = -1.5165390156 x = -1.5165390156 Simplifying x = -1.5165390156Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6593961584, -1.5165390156}
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