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Simplifying 7x2 + -2 = 6x + 2 Reorder the terms: -2 + 7x2 = 6x + 2 Reorder the terms: -2 + 7x2 = 2 + 6x Solving -2 + 7x2 = 2 + 6x Solving for variable 'x'. Reorder the terms: -2 + -2 + -6x + 7x2 = 2 + 6x + -2 + -6x Combine like terms: -2 + -2 = -4 -4 + -6x + 7x2 = 2 + 6x + -2 + -6x Reorder the terms: -4 + -6x + 7x2 = 2 + -2 + 6x + -6x Combine like terms: 2 + -2 = 0 -4 + -6x + 7x2 = 0 + 6x + -6x -4 + -6x + 7x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -4 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.8571428571x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.8571428571x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.5714285714 -0.8571428571x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.8571428571x + x2 = 0.5714285714 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 = 0.5714285714 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.5714285714 + 0.1836734694 Combine like terms: 0.5714285714 + 0.1836734694 = 0.7551020408 0.1836734694 + -0.8571428571x + x2 = 0.7551020408 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 0.7551020408 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 0.868966076 and -0.868966076.Subproblem 1
x + -0.4285714286 = 0.868966076 Simplifying x + -0.4285714286 = 0.868966076 Reorder the terms: -0.4285714286 + x = 0.868966076 Solving -0.4285714286 + x = 0.868966076 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 = 0.868966076 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 0.868966076 + 0.4285714286 x = 0.868966076 + 0.4285714286 Combine like terms: 0.868966076 + 0.4285714286 = 1.2975375046 x = 1.2975375046 Simplifying x = 1.2975375046Subproblem 2
x + -0.4285714286 = -0.868966076 Simplifying x + -0.4285714286 = -0.868966076 Reorder the terms: -0.4285714286 + x = -0.868966076 Solving -0.4285714286 + x = -0.868966076 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 = -0.868966076 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -0.868966076 + 0.4285714286 x = -0.868966076 + 0.4285714286 Combine like terms: -0.868966076 + 0.4285714286 = -0.4403946474 x = -0.4403946474 Simplifying x = -0.4403946474Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2975375046, -0.4403946474}
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