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Simplifying 9x2 + 18x + -45 = 5 Reorder the terms: -45 + 18x + 9x2 = 5 Solving -45 + 18x + 9x2 = 5 Solving for variable 'x'. Reorder the terms: -45 + -5 + 18x + 9x2 = 5 + -5 Combine like terms: -45 + -5 = -50 -50 + 18x + 9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -50 + 18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.555555556 + 2x + x2 = 0 Move the constant term to the right: Add '5.555555556' to each side of the equation. -5.555555556 + 2x + 5.555555556 + x2 = 0 + 5.555555556 Reorder the terms: -5.555555556 + 5.555555556 + 2x + x2 = 0 + 5.555555556 Combine like terms: -5.555555556 + 5.555555556 = 0.000000000 0.000000000 + 2x + x2 = 0 + 5.555555556 2x + x2 = 0 + 5.555555556 Combine like terms: 0 + 5.555555556 = 5.555555556 2x + x2 = 5.555555556 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 = 5.555555556 + 1 Reorder the terms: 1 + 2x + x2 = 5.555555556 + 1 Combine like terms: 5.555555556 + 1 = 6.555555556 1 + 2x + x2 = 6.555555556 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.555555556 Calculate the square root of the right side: 2.560381916 Break this problem into two subproblems by setting (x + 1) equal to 2.560381916 and -2.560381916.Subproblem 1
x + 1 = 2.560381916 Simplifying x + 1 = 2.560381916 Reorder the terms: 1 + x = 2.560381916 Solving 1 + x = 2.560381916 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 = 2.560381916 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.560381916 + -1 x = 2.560381916 + -1 Combine like terms: 2.560381916 + -1 = 1.560381916 x = 1.560381916 Simplifying x = 1.560381916Subproblem 2
x + 1 = -2.560381916 Simplifying x + 1 = -2.560381916 Reorder the terms: 1 + x = -2.560381916 Solving 1 + x = -2.560381916 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 = -2.560381916 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.560381916 + -1 x = -2.560381916 + -1 Combine like terms: -2.560381916 + -1 = -3.560381916 x = -3.560381916 Simplifying x = -3.560381916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560381916, -3.560381916}
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