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Simplifying x2 + 28x + 48 = 0 Reorder the terms: 48 + 28x + x2 = 0 Solving 48 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 28x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 28x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 28x + x2 = 0 + -48 28x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 28x + x2 = -48 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 = -48 + 196 Reorder the terms: 196 + 28x + x2 = -48 + 196 Combine like terms: -48 + 196 = 148 196 + 28x + x2 = 148 Factor a perfect square on the left side: (x + 14)(x + 14) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 14) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 14 = 12.165525061 Simplifying x + 14 = 12.165525061 Reorder the terms: 14 + x = 12.165525061 Solving 14 + x = 12.165525061 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 = 12.165525061 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.165525061 + -14 x = 12.165525061 + -14 Combine like terms: 12.165525061 + -14 = -1.834474939 x = -1.834474939 Simplifying x = -1.834474939Subproblem 2
x + 14 = -12.165525061 Simplifying x + 14 = -12.165525061 Reorder the terms: 14 + x = -12.165525061 Solving 14 + x = -12.165525061 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 = -12.165525061 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.165525061 + -14 x = -12.165525061 + -14 Combine like terms: -12.165525061 + -14 = -26.165525061 x = -26.165525061 Simplifying x = -26.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.834474939, -26.165525061}
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