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Simplifying 7x2 + -11x = 23 Reorder the terms: -11x + 7x2 = 23 Solving -11x + 7x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -11x + 7x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.285714286 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '3.285714286' to each side of the equation. -3.285714286 + -1.571428571x + 3.285714286 + x2 = 0 + 3.285714286 Reorder the terms: -3.285714286 + 3.285714286 + -1.571428571x + x2 = 0 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + -1.571428571x + x2 = 0 + 3.285714286 -1.571428571x + x2 = 0 + 3.285714286 Combine like terms: 0 + 3.285714286 = 3.285714286 -1.571428571x + x2 = 3.285714286 The x term is -1.571428571x. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571x + 0.6173469384 + x2 = 3.285714286 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = 3.285714286 + 0.6173469384 Combine like terms: 3.285714286 + 0.6173469384 = 3.9030612244 0.6173469384 + -1.571428571x + x2 = 3.9030612244 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 3.9030612244 Calculate the square root of the right side: 1.975616669 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 1.975616669 and -1.975616669.Subproblem 1
x + -0.7857142855 = 1.975616669 Simplifying x + -0.7857142855 = 1.975616669 Reorder the terms: -0.7857142855 + x = 1.975616669 Solving -0.7857142855 + x = 1.975616669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 1.975616669 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 1.975616669 + 0.7857142855 x = 1.975616669 + 0.7857142855 Combine like terms: 1.975616669 + 0.7857142855 = 2.7613309545 x = 2.7613309545 Simplifying x = 2.7613309545Subproblem 2
x + -0.7857142855 = -1.975616669 Simplifying x + -0.7857142855 = -1.975616669 Reorder the terms: -0.7857142855 + x = -1.975616669 Solving -0.7857142855 + x = -1.975616669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -1.975616669 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -1.975616669 + 0.7857142855 x = -1.975616669 + 0.7857142855 Combine like terms: -1.975616669 + 0.7857142855 = -1.1899023835 x = -1.1899023835 Simplifying x = -1.1899023835Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7613309545, -1.1899023835}
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