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Simplifying x2 + 14x + -370 = 0 Reorder the terms: -370 + 14x + x2 = 0 Solving -370 + 14x + 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 + 14x + 370 + x2 = 0 + 370 Reorder the terms: -370 + 370 + 14x + x2 = 0 + 370 Combine like terms: -370 + 370 = 0 0 + 14x + x2 = 0 + 370 14x + x2 = 0 + 370 Combine like terms: 0 + 370 = 370 14x + x2 = 370 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 = 370 + 49 Reorder the terms: 49 + 14x + x2 = 370 + 49 Combine like terms: 370 + 49 = 419 49 + 14x + x2 = 419 Factor a perfect square on the left side: (x + 7)(x + 7) = 419 Calculate the square root of the right side: 20.46948949 Break this problem into two subproblems by setting (x + 7) equal to 20.46948949 and -20.46948949.Subproblem 1
x + 7 = 20.46948949 Simplifying x + 7 = 20.46948949 Reorder the terms: 7 + x = 20.46948949 Solving 7 + x = 20.46948949 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 = 20.46948949 + -7 Combine like terms: 7 + -7 = 0 0 + x = 20.46948949 + -7 x = 20.46948949 + -7 Combine like terms: 20.46948949 + -7 = 13.46948949 x = 13.46948949 Simplifying x = 13.46948949Subproblem 2
x + 7 = -20.46948949 Simplifying x + 7 = -20.46948949 Reorder the terms: 7 + x = -20.46948949 Solving 7 + x = -20.46948949 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 = -20.46948949 + -7 Combine like terms: 7 + -7 = 0 0 + x = -20.46948949 + -7 x = -20.46948949 + -7 Combine like terms: -20.46948949 + -7 = -27.46948949 x = -27.46948949 Simplifying x = -27.46948949Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.46948949, -27.46948949}
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