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Simplifying 0 = 18x2 + 90x + -43 Reorder the terms: 0 = -43 + 90x + 18x2 Solving 0 = -43 + 90x + 18x2 Solving for variable 'x'. Combine like terms: 0 + 43 = 43 43 + -90x + -18x2 = -43 + 90x + 18x2 + 43 + -90x + -18x2 Reorder the terms: 43 + -90x + -18x2 = -43 + 43 + 90x + -90x + 18x2 + -18x2 Combine like terms: -43 + 43 = 0 43 + -90x + -18x2 = 0 + 90x + -90x + 18x2 + -18x2 43 + -90x + -18x2 = 90x + -90x + 18x2 + -18x2 Combine like terms: 90x + -90x = 0 43 + -90x + -18x2 = 0 + 18x2 + -18x2 43 + -90x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 43 + -90x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -2.388888889 + 5x + x2 = 0 Move the constant term to the right: Add '2.388888889' to each side of the equation. -2.388888889 + 5x + 2.388888889 + x2 = 0 + 2.388888889 Reorder the terms: -2.388888889 + 2.388888889 + 5x + x2 = 0 + 2.388888889 Combine like terms: -2.388888889 + 2.388888889 = 0.000000000 0.000000000 + 5x + x2 = 0 + 2.388888889 5x + x2 = 0 + 2.388888889 Combine like terms: 0 + 2.388888889 = 2.388888889 5x + x2 = 2.388888889 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 2.388888889 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2.388888889 + 6.25 Combine like terms: 2.388888889 + 6.25 = 8.638888889 6.25 + 5x + x2 = 8.638888889 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 8.638888889 Calculate the square root of the right side: 2.939198681 Break this problem into two subproblems by setting (x + 2.5) equal to 2.939198681 and -2.939198681.Subproblem 1
x + 2.5 = 2.939198681 Simplifying x + 2.5 = 2.939198681 Reorder the terms: 2.5 + x = 2.939198681 Solving 2.5 + x = 2.939198681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.939198681 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.939198681 + -2.5 x = 2.939198681 + -2.5 Combine like terms: 2.939198681 + -2.5 = 0.439198681 x = 0.439198681 Simplifying x = 0.439198681Subproblem 2
x + 2.5 = -2.939198681 Simplifying x + 2.5 = -2.939198681 Reorder the terms: 2.5 + x = -2.939198681 Solving 2.5 + x = -2.939198681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.939198681 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.939198681 + -2.5 x = -2.939198681 + -2.5 Combine like terms: -2.939198681 + -2.5 = -5.439198681 x = -5.439198681 Simplifying x = -5.439198681Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.439198681, -5.439198681}
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