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Simplifying 0 = -7x2 + 9x + 7 Reorder the terms: 0 = 7 + 9x + -7x2 Solving 0 = 7 + 9x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -9x + 7x2 = 7 + 9x + -7x2 + -7 + -9x + 7x2 Reorder the terms: -7 + -9x + 7x2 = 7 + -7 + 9x + -9x + -7x2 + 7x2 Combine like terms: 7 + -7 = 0 -7 + -9x + 7x2 = 0 + 9x + -9x + -7x2 + 7x2 -7 + -9x + 7x2 = 9x + -9x + -7x2 + 7x2 Combine like terms: 9x + -9x = 0 -7 + -9x + 7x2 = 0 + -7x2 + 7x2 -7 + -9x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -7 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.285714286x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.285714286x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.285714286x + x2 = 0 + 1 -1.285714286x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.285714286x + x2 = 1 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 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1 + 0.4132653063 Combine like terms: 1 + 0.4132653063 = 1.4132653063 0.4132653063 + -1.285714286x + x2 = 1.4132653063 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.4132653063 Calculate the square root of the right side: 1.188808356 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.188808356 and -1.188808356.Subproblem 1
x + -0.642857143 = 1.188808356 Simplifying x + -0.642857143 = 1.188808356 Reorder the terms: -0.642857143 + x = 1.188808356 Solving -0.642857143 + x = 1.188808356 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 = 1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.188808356 + 0.642857143 x = 1.188808356 + 0.642857143 Combine like terms: 1.188808356 + 0.642857143 = 1.831665499 x = 1.831665499 Simplifying x = 1.831665499Subproblem 2
x + -0.642857143 = -1.188808356 Simplifying x + -0.642857143 = -1.188808356 Reorder the terms: -0.642857143 + x = -1.188808356 Solving -0.642857143 + x = -1.188808356 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 = -1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.188808356 + 0.642857143 x = -1.188808356 + 0.642857143 Combine like terms: -1.188808356 + 0.642857143 = -0.545951213 x = -0.545951213 Simplifying x = -0.545951213Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.831665499, -0.545951213}
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