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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 = 206 225 + 30x + x2 = 206 Factor a perfect square on the left side: (x + 15)(x + 15) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 15) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 15 = 14.352700094 Simplifying x + 15 = 14.352700094 Reorder the terms: 15 + x = 14.352700094 Solving 15 + x = 14.352700094 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 = 14.352700094 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.352700094 + -15 x = 14.352700094 + -15 Combine like terms: 14.352700094 + -15 = -0.647299906 x = -0.647299906 Simplifying x = -0.647299906Subproblem 2
x + 15 = -14.352700094 Simplifying x + 15 = -14.352700094 Reorder the terms: 15 + x = -14.352700094 Solving 15 + x = -14.352700094 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 = -14.352700094 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.352700094 + -15 x = -14.352700094 + -15 Combine like terms: -14.352700094 + -15 = -29.352700094 x = -29.352700094 Simplifying x = -29.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.647299906, -29.352700094}
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