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Simplifying 7x2 + 6x + -14 = 0 Reorder the terms: -14 + 6x + 7x2 = 0 Solving -14 + 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'. -2 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.8571428571x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.8571428571x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.8571428571x + x2 = 0 + 2 0.8571428571x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.8571428571x + x2 = 2 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 = 2 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = 2 + 0.1836734694 Combine like terms: 2 + 0.1836734694 = 2.1836734694 0.1836734694 + 0.8571428571x + x2 = 2.1836734694 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = 2.1836734694 Calculate the square root of the right side: 1.477725776 Break this problem into two subproblems by setting (x + 0.4285714286) equal to 1.477725776 and -1.477725776.Subproblem 1
x + 0.4285714286 = 1.477725776 Simplifying x + 0.4285714286 = 1.477725776 Reorder the terms: 0.4285714286 + x = 1.477725776 Solving 0.4285714286 + x = 1.477725776 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 = 1.477725776 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = 1.477725776 + -0.4285714286 x = 1.477725776 + -0.4285714286 Combine like terms: 1.477725776 + -0.4285714286 = 1.0491543474 x = 1.0491543474 Simplifying x = 1.0491543474Subproblem 2
x + 0.4285714286 = -1.477725776 Simplifying x + 0.4285714286 = -1.477725776 Reorder the terms: 0.4285714286 + x = -1.477725776 Solving 0.4285714286 + x = -1.477725776 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 = -1.477725776 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + x = -1.477725776 + -0.4285714286 x = -1.477725776 + -0.4285714286 Combine like terms: -1.477725776 + -0.4285714286 = -1.9062972046 x = -1.9062972046 Simplifying x = -1.9062972046Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0491543474, -1.9062972046}
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