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Simplifying (1.7x * 1.7x) + 24x + 45 = 0 Reorder the terms for easier multiplication: (1.7 * 1.7x * x) + 24x + 45 = 0 Multiply 1.7 * 1.7 (2.89x * x) + 24x + 45 = 0 Multiply x * x (2.89x2) + 24x + 45 = 0 Reorder the terms: 45 + 24x + (2.89x2) = 0 Solving 45 + 24x + (2.89x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.89 the coefficient of the squared term: Divide each side by '2.89'. 15.57093426 + 8.30449827x + x2 = 0 Move the constant term to the right: Add '-15.57093426' to each side of the equation. 15.57093426 + 8.30449827x + -15.57093426 + x2 = 0 + -15.57093426 Reorder the terms: 15.57093426 + -15.57093426 + 8.30449827x + x2 = 0 + -15.57093426 Combine like terms: 15.57093426 + -15.57093426 = 0.00000000 0.00000000 + 8.30449827x + x2 = 0 + -15.57093426 8.30449827x + x2 = 0 + -15.57093426 Combine like terms: 0 + -15.57093426 = -15.57093426 8.30449827x + x2 = -15.57093426 The x term is 8.30449827x. Take half its coefficient (4.152249135). Square it (17.24117288) and add it to both sides. Add '17.24117288' to each side of the equation. 8.30449827x + 17.24117288 + x2 = -15.57093426 + 17.24117288 Reorder the terms: 17.24117288 + 8.30449827x + x2 = -15.57093426 + 17.24117288 Combine like terms: -15.57093426 + 17.24117288 = 1.67023862 17.24117288 + 8.30449827x + x2 = 1.67023862 Factor a perfect square on the left side: ((x) + 4.152249135)((x) + 4.152249135) = 1.67023862 Calculate the square root of the right side: 1.29237712 Break this problem into two subproblems by setting ((x) + 4.152249135) equal to 1.29237712 and -1.29237712.Subproblem 1
(x) + 4.152249135 = 1.29237712 Simplifying (x) + 4.152249135 = 1.29237712 x + 4.152249135 = 1.29237712 Reorder the terms: 4.152249135 + x = 1.29237712 Solving 4.152249135 + x = 1.29237712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.152249135' to each side of the equation. 4.152249135 + -4.152249135 + x = 1.29237712 + -4.152249135 Combine like terms: 4.152249135 + -4.152249135 = 0.000000000 0.000000000 + x = 1.29237712 + -4.152249135 x = 1.29237712 + -4.152249135 Combine like terms: 1.29237712 + -4.152249135 = -2.859872015 x = -2.859872015 Simplifying x = -2.859872015Subproblem 2
(x) + 4.152249135 = -1.29237712 Simplifying (x) + 4.152249135 = -1.29237712 x + 4.152249135 = -1.29237712 Reorder the terms: 4.152249135 + x = -1.29237712 Solving 4.152249135 + x = -1.29237712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.152249135' to each side of the equation. 4.152249135 + -4.152249135 + x = -1.29237712 + -4.152249135 Combine like terms: 4.152249135 + -4.152249135 = 0.000000000 0.000000000 + x = -1.29237712 + -4.152249135 x = -1.29237712 + -4.152249135 Combine like terms: -1.29237712 + -4.152249135 = -5.444626255 x = -5.444626255 Simplifying x = -5.444626255Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.859872015, -5.444626255}
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