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Simplifying 7x2 + -6x + -196 = 0 Reorder the terms: -196 + -6x + 7x2 = 0 Solving -196 + -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'. -28 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -0.8571428571x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -0.8571428571x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -0.8571428571x + x2 = 0 + 28 -0.8571428571x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -0.8571428571x + x2 = 28 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 = 28 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 28 + 0.1836734694 Combine like terms: 28 + 0.1836734694 = 28.1836734694 0.1836734694 + -0.8571428571x + x2 = 28.1836734694 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 28.1836734694 Calculate the square root of the right side: 5.308829765 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 5.308829765 and -5.308829765.Subproblem 1
x + -0.4285714286 = 5.308829765 Simplifying x + -0.4285714286 = 5.308829765 Reorder the terms: -0.4285714286 + x = 5.308829765 Solving -0.4285714286 + x = 5.308829765 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 = 5.308829765 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 5.308829765 + 0.4285714286 x = 5.308829765 + 0.4285714286 Combine like terms: 5.308829765 + 0.4285714286 = 5.7374011936 x = 5.7374011936 Simplifying x = 5.7374011936Subproblem 2
x + -0.4285714286 = -5.308829765 Simplifying x + -0.4285714286 = -5.308829765 Reorder the terms: -0.4285714286 + x = -5.308829765 Solving -0.4285714286 + x = -5.308829765 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 = -5.308829765 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -5.308829765 + 0.4285714286 x = -5.308829765 + 0.4285714286 Combine like terms: -5.308829765 + 0.4285714286 = -4.8802583364 x = -4.8802583364 Simplifying x = -4.8802583364Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.7374011936, -4.8802583364}
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