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Simplifying 5x2 + -18x + -210 = 0 Reorder the terms: -210 + -18x + 5x2 = 0 Solving -210 + -18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -42 + -3.6x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -3.6x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -3.6x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -3.6x + x2 = 0 + 42 -3.6x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -3.6x + x2 = 42 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 42 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 42 + 3.24 Combine like terms: 42 + 3.24 = 45.24 3.24 + -3.6x + x2 = 45.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 45.24 Calculate the square root of the right side: 6.726068688 Break this problem into two subproblems by setting (x + -1.8) equal to 6.726068688 and -6.726068688.Subproblem 1
x + -1.8 = 6.726068688 Simplifying x + -1.8 = 6.726068688 Reorder the terms: -1.8 + x = 6.726068688 Solving -1.8 + x = 6.726068688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 6.726068688 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 6.726068688 + 1.8 x = 6.726068688 + 1.8 Combine like terms: 6.726068688 + 1.8 = 8.526068688 x = 8.526068688 Simplifying x = 8.526068688Subproblem 2
x + -1.8 = -6.726068688 Simplifying x + -1.8 = -6.726068688 Reorder the terms: -1.8 + x = -6.726068688 Solving -1.8 + x = -6.726068688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -6.726068688 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -6.726068688 + 1.8 x = -6.726068688 + 1.8 Combine like terms: -6.726068688 + 1.8 = -4.926068688 x = -4.926068688 Simplifying x = -4.926068688Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.526068688, -4.926068688}
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