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Simplifying 7x2 + -9x + -11 = 0 Reorder the terms: -11 + -9x + 7x2 = 0 Solving -11 + -9x + 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'. -1.571428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -1.285714286x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -1.285714286x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 1.571428571 -1.285714286x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -1.285714286x + x2 = 1.571428571 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 1.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1.571428571 + 0.4132653063 Combine like terms: 1.571428571 + 0.4132653063 = 1.9846938773 0.4132653063 + -1.285714286x + x2 = 1.9846938773 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.9846938773 Calculate the square root of the right side: 1.408791637 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.408791637 and -1.408791637.Subproblem 1
x + -0.642857143 = 1.408791637 Simplifying x + -0.642857143 = 1.408791637 Reorder the terms: -0.642857143 + x = 1.408791637 Solving -0.642857143 + x = 1.408791637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 1.408791637 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.408791637 + 0.642857143 x = 1.408791637 + 0.642857143 Combine like terms: 1.408791637 + 0.642857143 = 2.05164878 x = 2.05164878 Simplifying x = 2.05164878Subproblem 2
x + -0.642857143 = -1.408791637 Simplifying x + -0.642857143 = -1.408791637 Reorder the terms: -0.642857143 + x = -1.408791637 Solving -0.642857143 + x = -1.408791637 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -1.408791637 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.408791637 + 0.642857143 x = -1.408791637 + 0.642857143 Combine like terms: -1.408791637 + 0.642857143 = -0.765934494 x = -0.765934494 Simplifying x = -0.765934494Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.05164878, -0.765934494}
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