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Simplifying 5x2 + -18x = 1225 Reorder the terms: -18x + 5x2 = 1225 Solving -18x + 5x2 = 1225 Solving for variable 'x'. Reorder the terms: -1225 + -18x + 5x2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1225 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -245 + -3.6x + x2 = 0 Move the constant term to the right: Add '245' to each side of the equation. -245 + -3.6x + 245 + x2 = 0 + 245 Reorder the terms: -245 + 245 + -3.6x + x2 = 0 + 245 Combine like terms: -245 + 245 = 0 0 + -3.6x + x2 = 0 + 245 -3.6x + x2 = 0 + 245 Combine like terms: 0 + 245 = 245 -3.6x + x2 = 245 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 = 245 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 245 + 3.24 Combine like terms: 245 + 3.24 = 248.24 3.24 + -3.6x + x2 = 248.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 248.24 Calculate the square root of the right side: 15.755633913 Break this problem into two subproblems by setting (x + -1.8) equal to 15.755633913 and -15.755633913.Subproblem 1
x + -1.8 = 15.755633913 Simplifying x + -1.8 = 15.755633913 Reorder the terms: -1.8 + x = 15.755633913 Solving -1.8 + x = 15.755633913 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 = 15.755633913 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 15.755633913 + 1.8 x = 15.755633913 + 1.8 Combine like terms: 15.755633913 + 1.8 = 17.555633913 x = 17.555633913 Simplifying x = 17.555633913Subproblem 2
x + -1.8 = -15.755633913 Simplifying x + -1.8 = -15.755633913 Reorder the terms: -1.8 + x = -15.755633913 Solving -1.8 + x = -15.755633913 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 = -15.755633913 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -15.755633913 + 1.8 x = -15.755633913 + 1.8 Combine like terms: -15.755633913 + 1.8 = -13.955633913 x = -13.955633913 Simplifying x = -13.955633913Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.555633913, -13.955633913}
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