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Simplifying x2 + 28x + -9 = 0 Reorder the terms: -9 + 28x + x2 = 0 Solving -9 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 28x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 28x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 28x + x2 = 0 + 9 28x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 28x + x2 = 9 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 9 + 196 Reorder the terms: 196 + 28x + x2 = 9 + 196 Combine like terms: 9 + 196 = 205 196 + 28x + x2 = 205 Factor a perfect square on the left side: (x + 14)(x + 14) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 14) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 14 = 14.317821063 Simplifying x + 14 = 14.317821063 Reorder the terms: 14 + x = 14.317821063 Solving 14 + x = 14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 14.317821063 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.317821063 + -14 x = 14.317821063 + -14 Combine like terms: 14.317821063 + -14 = 0.317821063 x = 0.317821063 Simplifying x = 0.317821063Subproblem 2
x + 14 = -14.317821063 Simplifying x + 14 = -14.317821063 Reorder the terms: 14 + x = -14.317821063 Solving 14 + x = -14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -14.317821063 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.317821063 + -14 x = -14.317821063 + -14 Combine like terms: -14.317821063 + -14 = -28.317821063 x = -28.317821063 Simplifying x = -28.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.317821063, -28.317821063}
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