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Simplifying 5x2 + -18x + 81 = 90 Reorder the terms: 81 + -18x + 5x2 = 90 Solving 81 + -18x + 5x2 = 90 Solving for variable 'x'. Reorder the terms: 81 + -90 + -18x + 5x2 = 90 + -90 Combine like terms: 81 + -90 = -9 -9 + -18x + 5x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -9 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -3.6x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -3.6x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -3.6x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -3.6x + x2 = 0 + 1.8 -3.6x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -3.6x + x2 = 1.8 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 = 1.8 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 1.8 + 3.24 Combine like terms: 1.8 + 3.24 = 5.04 3.24 + -3.6x + x2 = 5.04 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (x + -1.8) equal to 2.244994432 and -2.244994432.Subproblem 1
x + -1.8 = 2.244994432 Simplifying x + -1.8 = 2.244994432 Reorder the terms: -1.8 + x = 2.244994432 Solving -1.8 + x = 2.244994432 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 = 2.244994432 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.244994432 + 1.8 x = 2.244994432 + 1.8 Combine like terms: 2.244994432 + 1.8 = 4.044994432 x = 4.044994432 Simplifying x = 4.044994432Subproblem 2
x + -1.8 = -2.244994432 Simplifying x + -1.8 = -2.244994432 Reorder the terms: -1.8 + x = -2.244994432 Solving -1.8 + x = -2.244994432 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 = -2.244994432 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.244994432 + 1.8 x = -2.244994432 + 1.8 Combine like terms: -2.244994432 + 1.8 = -0.444994432 x = -0.444994432 Simplifying x = -0.444994432Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.044994432, -0.444994432}
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