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Simplifying 49x2 + 42x = 17 Reorder the terms: 42x + 49x2 = 17 Solving 42x + 49x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 42x + 49x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 42x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.3469387755 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.3469387755' to each side of the equation. -0.3469387755 + 0.8571428571x + 0.3469387755 + x2 = 0 + 0.3469387755 Reorder the terms: -0.3469387755 + 0.3469387755 + 0.8571428571x + x2 = 0 + 0.3469387755 Combine like terms: -0.3469387755 + 0.3469387755 = 0.0000000000 0.0000000000 + 0.8571428571x + x2 = 0 + 0.3469387755 0.8571428571x + x2 = 0 + 0.3469387755 Combine like terms: 0 + 0.3469387755 = 0.3469387755 0.8571428571x + x2 = 0.3469387755 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 = 0.3469387755 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 0.3469387755 + 0.1836734694 Combine like terms: 0.3469387755 + 0.1836734694 = 0.5306122449 0.1836734694 + 0.8571428571x + x2 = 0.5306122449 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 0.5306122449 Calculate the square root of the right side: 0.728431359 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 0.728431359 and -0.728431359.Subproblem 1
x + 0.4285714286 = 0.728431359 Simplifying x + 0.4285714286 = 0.728431359 Reorder the terms: 0.4285714286 + x = 0.728431359 Solving 0.4285714286 + x = 0.728431359 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 = 0.728431359 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 0.728431359 + -0.4285714286 x = 0.728431359 + -0.4285714286 Combine like terms: 0.728431359 + -0.4285714286 = 0.2998599304 x = 0.2998599304 Simplifying x = 0.2998599304Subproblem 2
x + 0.4285714286 = -0.728431359 Simplifying x + 0.4285714286 = -0.728431359 Reorder the terms: 0.4285714286 + x = -0.728431359 Solving 0.4285714286 + x = -0.728431359 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 = -0.728431359 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -0.728431359 + -0.4285714286 x = -0.728431359 + -0.4285714286 Combine like terms: -0.728431359 + -0.4285714286 = -1.1570027876 x = -1.1570027876 Simplifying x = -1.1570027876Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2998599304, -1.1570027876}
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