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Simplifying x2 + 28x + 100 = 0 Reorder the terms: 100 + 28x + x2 = 0 Solving 100 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 28x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 28x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 28x + x2 = 0 + -100 28x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 28x + x2 = -100 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 = -100 + 196 Reorder the terms: 196 + 28x + x2 = -100 + 196 Combine like terms: -100 + 196 = 96 196 + 28x + x2 = 96 Factor a perfect square on the left side: (x + 14)(x + 14) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 14) equal to 9.797958971 and -9.797958971.Subproblem 1
x + 14 = 9.797958971 Simplifying x + 14 = 9.797958971 Reorder the terms: 14 + x = 9.797958971 Solving 14 + x = 9.797958971 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 = 9.797958971 + -14 Combine like terms: 14 + -14 = 0 0 + x = 9.797958971 + -14 x = 9.797958971 + -14 Combine like terms: 9.797958971 + -14 = -4.202041029 x = -4.202041029 Simplifying x = -4.202041029Subproblem 2
x + 14 = -9.797958971 Simplifying x + 14 = -9.797958971 Reorder the terms: 14 + x = -9.797958971 Solving 14 + x = -9.797958971 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 = -9.797958971 + -14 Combine like terms: 14 + -14 = 0 0 + x = -9.797958971 + -14 x = -9.797958971 + -14 Combine like terms: -9.797958971 + -14 = -23.797958971 x = -23.797958971 Simplifying x = -23.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.202041029, -23.797958971}
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