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Simplifying 5x2 + -18x = -11 Reorder the terms: -18x + 5x2 = -11 Solving -18x + 5x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -18x + 5x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.2 + -3.6x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -3.6x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -3.6x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -3.6x + x2 = 0 + -2.2 -3.6x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -3.6x + x2 = -2.2 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 = -2.2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -2.2 + 3.24 Combine like terms: -2.2 + 3.24 = 1.04 3.24 + -3.6x + x2 = 1.04 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + -1.8) equal to 1.019803903 and -1.019803903.Subproblem 1
x + -1.8 = 1.019803903 Simplifying x + -1.8 = 1.019803903 Reorder the terms: -1.8 + x = 1.019803903 Solving -1.8 + x = 1.019803903 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 = 1.019803903 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.019803903 + 1.8 x = 1.019803903 + 1.8 Combine like terms: 1.019803903 + 1.8 = 2.819803903 x = 2.819803903 Simplifying x = 2.819803903Subproblem 2
x + -1.8 = -1.019803903 Simplifying x + -1.8 = -1.019803903 Reorder the terms: -1.8 + x = -1.019803903 Solving -1.8 + x = -1.019803903 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 = -1.019803903 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.019803903 + 1.8 x = -1.019803903 + 1.8 Combine like terms: -1.019803903 + 1.8 = 0.780196097 x = 0.780196097 Simplifying x = 0.780196097Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.819803903, 0.780196097}
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