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Simplifying 7x2 + -9x + -6 = 8 Reorder the terms: -6 + -9x + 7x2 = 8 Solving -6 + -9x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -6 + -8 + -9x + 7x2 = 8 + -8 Combine like terms: -6 + -8 = -14 -14 + -9x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -14 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.285714286x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.285714286x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.285714286x + x2 = 0 + 2 -1.285714286x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.285714286x + x2 = 2 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 = 2 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 2 + 0.4132653063 Combine like terms: 2 + 0.4132653063 = 2.4132653063 0.4132653063 + -1.285714286x + x2 = 2.4132653063 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 2.4132653063 Calculate the square root of the right side: 1.553468798 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.553468798 and -1.553468798.Subproblem 1
x + -0.642857143 = 1.553468798 Simplifying x + -0.642857143 = 1.553468798 Reorder the terms: -0.642857143 + x = 1.553468798 Solving -0.642857143 + x = 1.553468798 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 = 1.553468798 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.553468798 + 0.642857143 x = 1.553468798 + 0.642857143 Combine like terms: 1.553468798 + 0.642857143 = 2.196325941 x = 2.196325941 Simplifying x = 2.196325941Subproblem 2
x + -0.642857143 = -1.553468798 Simplifying x + -0.642857143 = -1.553468798 Reorder the terms: -0.642857143 + x = -1.553468798 Solving -0.642857143 + x = -1.553468798 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 = -1.553468798 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.553468798 + 0.642857143 x = -1.553468798 + 0.642857143 Combine like terms: -1.553468798 + 0.642857143 = -0.910611655 x = -0.910611655 Simplifying x = -0.910611655Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.196325941, -0.910611655}
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