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Simplifying x2 + 30x + -6 = 0 Reorder the terms: -6 + 30x + x2 = 0 Solving -6 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 30x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 30x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 30x + x2 = 0 + 6 30x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 30x + x2 = 6 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 = 6 + 225 Reorder the terms: 225 + 30x + x2 = 6 + 225 Combine like terms: 6 + 225 = 231 225 + 30x + x2 = 231 Factor a perfect square on the left side: (x + 15)(x + 15) = 231 Calculate the square root of the right side: 15.198684154 Break this problem into two subproblems by setting (x + 15) equal to 15.198684154 and -15.198684154.Subproblem 1
x + 15 = 15.198684154 Simplifying x + 15 = 15.198684154 Reorder the terms: 15 + x = 15.198684154 Solving 15 + x = 15.198684154 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 = 15.198684154 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.198684154 + -15 x = 15.198684154 + -15 Combine like terms: 15.198684154 + -15 = 0.198684154 x = 0.198684154 Simplifying x = 0.198684154Subproblem 2
x + 15 = -15.198684154 Simplifying x + 15 = -15.198684154 Reorder the terms: 15 + x = -15.198684154 Solving 15 + x = -15.198684154 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 = -15.198684154 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.198684154 + -15 x = -15.198684154 + -15 Combine like terms: -15.198684154 + -15 = -30.198684154 x = -30.198684154 Simplifying x = -30.198684154Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198684154, -30.198684154}
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