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Simplifying 7x2 + -6x + -23 = 0 Reorder the terms: -23 + -6x + 7x2 = 0 Solving -23 + -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'. -3.285714286 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '3.285714286' to each side of the equation. -3.285714286 + -0.8571428571x + 3.285714286 + x2 = 0 + 3.285714286 Reorder the terms: -3.285714286 + 3.285714286 + -0.8571428571x + x2 = 0 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + -0.8571428571x + x2 = 0 + 3.285714286 -0.8571428571x + x2 = 0 + 3.285714286 Combine like terms: 0 + 3.285714286 = 3.285714286 -0.8571428571x + x2 = 3.285714286 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 = 3.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 3.285714286 + 0.1836734694 Combine like terms: 3.285714286 + 0.1836734694 = 3.4693877554 0.1836734694 + -0.8571428571x + x2 = 3.4693877554 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 3.4693877554 Calculate the square root of the right side: 1.862629259 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.862629259 and -1.862629259.Subproblem 1
x + -0.4285714286 = 1.862629259 Simplifying x + -0.4285714286 = 1.862629259 Reorder the terms: -0.4285714286 + x = 1.862629259 Solving -0.4285714286 + x = 1.862629259 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 = 1.862629259 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.862629259 + 0.4285714286 x = 1.862629259 + 0.4285714286 Combine like terms: 1.862629259 + 0.4285714286 = 2.2912006876 x = 2.2912006876 Simplifying x = 2.2912006876Subproblem 2
x + -0.4285714286 = -1.862629259 Simplifying x + -0.4285714286 = -1.862629259 Reorder the terms: -0.4285714286 + x = -1.862629259 Solving -0.4285714286 + x = -1.862629259 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 = -1.862629259 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.862629259 + 0.4285714286 x = -1.862629259 + 0.4285714286 Combine like terms: -1.862629259 + 0.4285714286 = -1.4340578304 x = -1.4340578304 Simplifying x = -1.4340578304Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2912006876, -1.4340578304}
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