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Simplifying x2 + 30x = -10 Reorder the terms: 30x + x2 = -10 Solving 30x + x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + 30x + x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 30x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 30x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 30x + x2 = 0 + -10 30x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 30x + x2 = -10 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 = -10 + 225 Reorder the terms: 225 + 30x + x2 = -10 + 225 Combine like terms: -10 + 225 = 215 225 + 30x + x2 = 215 Factor a perfect square on the left side: (x + 15)(x + 15) = 215 Calculate the square root of the right side: 14.662878299 Break this problem into two subproblems by setting (x + 15) equal to 14.662878299 and -14.662878299.Subproblem 1
x + 15 = 14.662878299 Simplifying x + 15 = 14.662878299 Reorder the terms: 15 + x = 14.662878299 Solving 15 + x = 14.662878299 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 = 14.662878299 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.662878299 + -15 x = 14.662878299 + -15 Combine like terms: 14.662878299 + -15 = -0.337121701 x = -0.337121701 Simplifying x = -0.337121701Subproblem 2
x + 15 = -14.662878299 Simplifying x + 15 = -14.662878299 Reorder the terms: 15 + x = -14.662878299 Solving 15 + x = -14.662878299 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 = -14.662878299 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.662878299 + -15 x = -14.662878299 + -15 Combine like terms: -14.662878299 + -15 = -29.662878299 x = -29.662878299 Simplifying x = -29.662878299Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.337121701, -29.662878299}
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