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Simplifying x2 + -30x + -19 = 0 Reorder the terms: -19 + -30x + x2 = 0 Solving -19 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -30x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -30x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -30x + x2 = 0 + 19 -30x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -30x + x2 = 19 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 19 + 225 Reorder the terms: 225 + -30x + x2 = 19 + 225 Combine like terms: 19 + 225 = 244 225 + -30x + x2 = 244 Factor a perfect square on the left side: (x + -15)(x + -15) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + -15) equal to 15.620499352 and -15.620499352.Subproblem 1
x + -15 = 15.620499352 Simplifying x + -15 = 15.620499352 Reorder the terms: -15 + x = 15.620499352 Solving -15 + x = 15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 15.620499352 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.620499352 + 15 x = 15.620499352 + 15 Combine like terms: 15.620499352 + 15 = 30.620499352 x = 30.620499352 Simplifying x = 30.620499352Subproblem 2
x + -15 = -15.620499352 Simplifying x + -15 = -15.620499352 Reorder the terms: -15 + x = -15.620499352 Solving -15 + x = -15.620499352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -15.620499352 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.620499352 + 15 x = -15.620499352 + 15 Combine like terms: -15.620499352 + 15 = -0.620499352 x = -0.620499352 Simplifying x = -0.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.620499352, -0.620499352}
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