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Simplifying x2 + 48x + 370 = 0 Reorder the terms: 370 + 48x + x2 = 0 Solving 370 + 48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-370' to each side of the equation. 370 + 48x + -370 + x2 = 0 + -370 Reorder the terms: 370 + -370 + 48x + x2 = 0 + -370 Combine like terms: 370 + -370 = 0 0 + 48x + x2 = 0 + -370 48x + x2 = 0 + -370 Combine like terms: 0 + -370 = -370 48x + x2 = -370 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = -370 + 576 Reorder the terms: 576 + 48x + x2 = -370 + 576 Combine like terms: -370 + 576 = 206 576 + 48x + x2 = 206 Factor a perfect square on the left side: (x + 24)(x + 24) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 24) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 24 = 14.352700094 Simplifying x + 24 = 14.352700094 Reorder the terms: 24 + x = 14.352700094 Solving 24 + x = 14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 14.352700094 + -24 Combine like terms: 24 + -24 = 0 0 + x = 14.352700094 + -24 x = 14.352700094 + -24 Combine like terms: 14.352700094 + -24 = -9.647299906 x = -9.647299906 Simplifying x = -9.647299906Subproblem 2
x + 24 = -14.352700094 Simplifying x + 24 = -14.352700094 Reorder the terms: 24 + x = -14.352700094 Solving 24 + x = -14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -14.352700094 + -24 Combine like terms: 24 + -24 = 0 0 + x = -14.352700094 + -24 x = -14.352700094 + -24 Combine like terms: -14.352700094 + -24 = -38.352700094 x = -38.352700094 Simplifying x = -38.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.647299906, -38.352700094}
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