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Simplifying x2 + 8x + 22x = -15 Reorder the terms: 8x + 22x + x2 = -15 Combine like terms: 8x + 22x = 30x 30x + x2 = -15 Solving 30x + x2 = -15 Solving for variable 'x'. Reorder the terms: 15 + 30x + x2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 30x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 30x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 30x + x2 = 0 + -15 30x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 30x + x2 = -15 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 = -15 + 225 Reorder the terms: 225 + 30x + x2 = -15 + 225 Combine like terms: -15 + 225 = 210 225 + 30x + x2 = 210 Factor a perfect square on the left side: (x + 15)(x + 15) = 210 Calculate the square root of the right side: 14.491376746 Break this problem into two subproblems by setting (x + 15) equal to 14.491376746 and -14.491376746.Subproblem 1
x + 15 = 14.491376746 Simplifying x + 15 = 14.491376746 Reorder the terms: 15 + x = 14.491376746 Solving 15 + x = 14.491376746 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 = 14.491376746 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.491376746 + -15 x = 14.491376746 + -15 Combine like terms: 14.491376746 + -15 = -0.508623254 x = -0.508623254 Simplifying x = -0.508623254Subproblem 2
x + 15 = -14.491376746 Simplifying x + 15 = -14.491376746 Reorder the terms: 15 + x = -14.491376746 Solving 15 + x = -14.491376746 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 = -14.491376746 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.491376746 + -15 x = -14.491376746 + -15 Combine like terms: -14.491376746 + -15 = -29.491376746 x = -29.491376746 Simplifying x = -29.491376746Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.508623254, -29.491376746}
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