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Simplifying 7x2 + 9x = -1 Reorder the terms: 9x + 7x2 = -1 Solving 9x + 7x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 9x + 7x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.285714286x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.285714286x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.285714286x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.285714286x + x2 = 0 + -0.1428571429 1.285714286x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.285714286x + x2 = -0.1428571429 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 = -0.1428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286x + x2 = -0.1428571429 + 0.4132653063 Combine like terms: -0.1428571429 + 0.4132653063 = 0.2704081634 0.4132653063 + 1.285714286x + x2 = 0.2704081634 Factor a perfect square on the left side: (x + 0.642857143)(x + 0.642857143) = 0.2704081634 Calculate the square root of the right side: 0.520007849 Break this problem into two subproblems by setting (x + 0.642857143) equal to 0.520007849 and -0.520007849.Subproblem 1
x + 0.642857143 = 0.520007849 Simplifying x + 0.642857143 = 0.520007849 Reorder the terms: 0.642857143 + x = 0.520007849 Solving 0.642857143 + x = 0.520007849 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 = 0.520007849 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 0.520007849 + -0.642857143 x = 0.520007849 + -0.642857143 Combine like terms: 0.520007849 + -0.642857143 = -0.122849294 x = -0.122849294 Simplifying x = -0.122849294Subproblem 2
x + 0.642857143 = -0.520007849 Simplifying x + 0.642857143 = -0.520007849 Reorder the terms: 0.642857143 + x = -0.520007849 Solving 0.642857143 + x = -0.520007849 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 = -0.520007849 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -0.520007849 + -0.642857143 x = -0.520007849 + -0.642857143 Combine like terms: -0.520007849 + -0.642857143 = -1.162864992 x = -1.162864992 Simplifying x = -1.162864992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.122849294, -1.162864992}
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