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Simplifying x2 + 28x = 19 Reorder the terms: 28x + x2 = 19 Solving 28x + x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 28x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 28x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 28x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 28x + x2 = 0 + 19 28x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 28x + x2 = 19 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 = 19 + 196 Reorder the terms: 196 + 28x + x2 = 19 + 196 Combine like terms: 19 + 196 = 215 196 + 28x + x2 = 215 Factor a perfect square on the left side: (x + 14)(x + 14) = 215 Calculate the square root of the right side: 14.662878299 Break this problem into two subproblems by setting (x + 14) equal to 14.662878299 and -14.662878299.Subproblem 1
x + 14 = 14.662878299 Simplifying x + 14 = 14.662878299 Reorder the terms: 14 + x = 14.662878299 Solving 14 + x = 14.662878299 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 = 14.662878299 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.662878299 + -14 x = 14.662878299 + -14 Combine like terms: 14.662878299 + -14 = 0.662878299 x = 0.662878299 Simplifying x = 0.662878299Subproblem 2
x + 14 = -14.662878299 Simplifying x + 14 = -14.662878299 Reorder the terms: 14 + x = -14.662878299 Solving 14 + x = -14.662878299 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 = -14.662878299 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.662878299 + -14 x = -14.662878299 + -14 Combine like terms: -14.662878299 + -14 = -28.662878299 x = -28.662878299 Simplifying x = -28.662878299Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.662878299, -28.662878299}
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