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Simplifying x2 + 14x + -374 = 0 Reorder the terms: -374 + 14x + x2 = 0 Solving -374 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '374' to each side of the equation. -374 + 14x + 374 + x2 = 0 + 374 Reorder the terms: -374 + 374 + 14x + x2 = 0 + 374 Combine like terms: -374 + 374 = 0 0 + 14x + x2 = 0 + 374 14x + x2 = 0 + 374 Combine like terms: 0 + 374 = 374 14x + x2 = 374 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 374 + 49 Reorder the terms: 49 + 14x + x2 = 374 + 49 Combine like terms: 374 + 49 = 423 49 + 14x + x2 = 423 Factor a perfect square on the left side: (x + 7)(x + 7) = 423 Calculate the square root of the right side: 20.566963801 Break this problem into two subproblems by setting (x + 7) equal to 20.566963801 and -20.566963801.Subproblem 1
x + 7 = 20.566963801 Simplifying x + 7 = 20.566963801 Reorder the terms: 7 + x = 20.566963801 Solving 7 + x = 20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 20.566963801 + -7 Combine like terms: 7 + -7 = 0 0 + x = 20.566963801 + -7 x = 20.566963801 + -7 Combine like terms: 20.566963801 + -7 = 13.566963801 x = 13.566963801 Simplifying x = 13.566963801Subproblem 2
x + 7 = -20.566963801 Simplifying x + 7 = -20.566963801 Reorder the terms: 7 + x = -20.566963801 Solving 7 + x = -20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -20.566963801 + -7 Combine like terms: 7 + -7 = 0 0 + x = -20.566963801 + -7 x = -20.566963801 + -7 Combine like terms: -20.566963801 + -7 = -27.566963801 x = -27.566963801 Simplifying x = -27.566963801Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.566963801, -27.566963801}
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