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Simplifying x2 + 28x + -147 = 0 Reorder the terms: -147 + 28x + x2 = 0 Solving -147 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 28x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 28x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 28x + x2 = 0 + 147 28x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 28x + x2 = 147 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 = 147 + 196 Reorder the terms: 196 + 28x + x2 = 147 + 196 Combine like terms: 147 + 196 = 343 196 + 28x + x2 = 343 Factor a perfect square on the left side: (x + 14)(x + 14) = 343 Calculate the square root of the right side: 18.520259177 Break this problem into two subproblems by setting (x + 14) equal to 18.520259177 and -18.520259177.Subproblem 1
x + 14 = 18.520259177 Simplifying x + 14 = 18.520259177 Reorder the terms: 14 + x = 18.520259177 Solving 14 + x = 18.520259177 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 = 18.520259177 + -14 Combine like terms: 14 + -14 = 0 0 + x = 18.520259177 + -14 x = 18.520259177 + -14 Combine like terms: 18.520259177 + -14 = 4.520259177 x = 4.520259177 Simplifying x = 4.520259177Subproblem 2
x + 14 = -18.520259177 Simplifying x + 14 = -18.520259177 Reorder the terms: 14 + x = -18.520259177 Solving 14 + x = -18.520259177 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 = -18.520259177 + -14 Combine like terms: 14 + -14 = 0 0 + x = -18.520259177 + -14 x = -18.520259177 + -14 Combine like terms: -18.520259177 + -14 = -32.520259177 x = -32.520259177 Simplifying x = -32.520259177Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.520259177, -32.520259177}
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