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Simplifying 7x2 + 6x = 4 Reorder the terms: 6x + 7x2 = 4 Solving 6x + 7x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 6x + 7x2 = 4 + -4 Combine like terms: 4 + -4 = 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 = 0.4403946474 x = 0.4403946474 Simplifying x = 0.4403946474Subproblem 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 = -1.2975375046 x = -1.2975375046 Simplifying x = -1.2975375046Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4403946474, -1.2975375046}
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