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Simplifying 0 = -7x2 + 6x + 9 Reorder the terms: 0 = 9 + 6x + -7x2 Solving 0 = 9 + 6x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -6x + 7x2 = 9 + 6x + -7x2 + -9 + -6x + 7x2 Reorder the terms: -9 + -6x + 7x2 = 9 + -9 + 6x + -6x + -7x2 + 7x2 Combine like terms: 9 + -9 = 0 -9 + -6x + 7x2 = 0 + 6x + -6x + -7x2 + 7x2 -9 + -6x + 7x2 = 6x + -6x + -7x2 + 7x2 Combine like terms: 6x + -6x = 0 -9 + -6x + 7x2 = 0 + -7x2 + 7x2 -9 + -6x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -9 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.8571428571x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.8571428571x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 1.285714286 -0.8571428571x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.8571428571x + x2 = 1.285714286 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 = 1.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 1.285714286 + 0.1836734694 Combine like terms: 1.285714286 + 0.1836734694 = 1.4693877554 0.1836734694 + -0.8571428571x + x2 = 1.4693877554 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 1.4693877554 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.212183054 and -1.212183054.Subproblem 1
x + -0.4285714286 = 1.212183054 Simplifying x + -0.4285714286 = 1.212183054 Reorder the terms: -0.4285714286 + x = 1.212183054 Solving -0.4285714286 + x = 1.212183054 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 = 1.212183054 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.212183054 + 0.4285714286 x = 1.212183054 + 0.4285714286 Combine like terms: 1.212183054 + 0.4285714286 = 1.6407544826 x = 1.6407544826 Simplifying x = 1.6407544826Subproblem 2
x + -0.4285714286 = -1.212183054 Simplifying x + -0.4285714286 = -1.212183054 Reorder the terms: -0.4285714286 + x = -1.212183054 Solving -0.4285714286 + x = -1.212183054 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 = -1.212183054 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.212183054 + 0.4285714286 x = -1.212183054 + 0.4285714286 Combine like terms: -1.212183054 + 0.4285714286 = -0.7836116254 x = -0.7836116254 Simplifying x = -0.7836116254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6407544826, -0.7836116254}
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