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Simplifying x2 + 28x + 21 = 0 Reorder the terms: 21 + 28x + x2 = 0 Solving 21 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 28x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 28x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 28x + x2 = 0 + -21 28x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 28x + x2 = -21 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 = -21 + 196 Reorder the terms: 196 + 28x + x2 = -21 + 196 Combine like terms: -21 + 196 = 175 196 + 28x + x2 = 175 Factor a perfect square on the left side: (x + 14)(x + 14) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + 14) equal to 13.228756555 and -13.228756555.Subproblem 1
x + 14 = 13.228756555 Simplifying x + 14 = 13.228756555 Reorder the terms: 14 + x = 13.228756555 Solving 14 + x = 13.228756555 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 = 13.228756555 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.228756555 + -14 x = 13.228756555 + -14 Combine like terms: 13.228756555 + -14 = -0.771243445 x = -0.771243445 Simplifying x = -0.771243445Subproblem 2
x + 14 = -13.228756555 Simplifying x + 14 = -13.228756555 Reorder the terms: 14 + x = -13.228756555 Solving 14 + x = -13.228756555 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 = -13.228756555 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.228756555 + -14 x = -13.228756555 + -14 Combine like terms: -13.228756555 + -14 = -27.228756555 x = -27.228756555 Simplifying x = -27.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.771243445, -27.228756555}
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