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Simplifying 9x2 + 18x + -72 = -7 Reorder the terms: -72 + 18x + 9x2 = -7 Solving -72 + 18x + 9x2 = -7 Solving for variable 'x'. Reorder the terms: -72 + 7 + 18x + 9x2 = -7 + 7 Combine like terms: -72 + 7 = -65 -65 + 18x + 9x2 = -7 + 7 Combine like terms: -7 + 7 = 0 -65 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.222222222 + 2x + x2 = 0 Move the constant term to the right: Add '7.222222222' to each side of the equation. -7.222222222 + 2x + 7.222222222 + x2 = 0 + 7.222222222 Reorder the terms: -7.222222222 + 7.222222222 + 2x + x2 = 0 + 7.222222222 Combine like terms: -7.222222222 + 7.222222222 = 0.000000000 0.000000000 + 2x + x2 = 0 + 7.222222222 2x + x2 = 0 + 7.222222222 Combine like terms: 0 + 7.222222222 = 7.222222222 2x + x2 = 7.222222222 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 7.222222222 + 1 Reorder the terms: 1 + 2x + x2 = 7.222222222 + 1 Combine like terms: 7.222222222 + 1 = 8.222222222 1 + 2x + x2 = 8.222222222 Factor a perfect square on the left side: (x + 1)(x + 1) = 8.222222222 Calculate the square root of the right side: 2.867441756 Break this problem into two subproblems by setting (x + 1) equal to 2.867441756 and -2.867441756.Subproblem 1
x + 1 = 2.867441756 Simplifying x + 1 = 2.867441756 Reorder the terms: 1 + x = 2.867441756 Solving 1 + x = 2.867441756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.867441756 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.867441756 + -1 x = 2.867441756 + -1 Combine like terms: 2.867441756 + -1 = 1.867441756 x = 1.867441756 Simplifying x = 1.867441756Subproblem 2
x + 1 = -2.867441756 Simplifying x + 1 = -2.867441756 Reorder the terms: 1 + x = -2.867441756 Solving 1 + x = -2.867441756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.867441756 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.867441756 + -1 x = -2.867441756 + -1 Combine like terms: -2.867441756 + -1 = -3.867441756 x = -3.867441756 Simplifying x = -3.867441756Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.867441756, -3.867441756}
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