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Simplifying 2x2 + -14x + -343 = 0 Reorder the terms: -343 + -14x + 2x2 = 0 Solving -343 + -14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -171.5 + -7x + x2 = 0 Move the constant term to the right: Add '171.5' to each side of the equation. -171.5 + -7x + 171.5 + x2 = 0 + 171.5 Reorder the terms: -171.5 + 171.5 + -7x + x2 = 0 + 171.5 Combine like terms: -171.5 + 171.5 = 0.0 0.0 + -7x + x2 = 0 + 171.5 -7x + x2 = 0 + 171.5 Combine like terms: 0 + 171.5 = 171.5 -7x + x2 = 171.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 171.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 171.5 + 12.25 Combine like terms: 171.5 + 12.25 = 183.75 12.25 + -7x + x2 = 183.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 183.75 Calculate the square root of the right side: 13.555441712 Break this problem into two subproblems by setting (x + -3.5) equal to 13.555441712 and -13.555441712.Subproblem 1
x + -3.5 = 13.555441712 Simplifying x + -3.5 = 13.555441712 Reorder the terms: -3.5 + x = 13.555441712 Solving -3.5 + x = 13.555441712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 13.555441712 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 13.555441712 + 3.5 x = 13.555441712 + 3.5 Combine like terms: 13.555441712 + 3.5 = 17.055441712 x = 17.055441712 Simplifying x = 17.055441712Subproblem 2
x + -3.5 = -13.555441712 Simplifying x + -3.5 = -13.555441712 Reorder the terms: -3.5 + x = -13.555441712 Solving -3.5 + x = -13.555441712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -13.555441712 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -13.555441712 + 3.5 x = -13.555441712 + 3.5 Combine like terms: -13.555441712 + 3.5 = -10.055441712 x = -10.055441712 Simplifying x = -10.055441712Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.055441712, -10.055441712}
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