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Simplifying 2x2 + -14x + 7 = 0 Reorder the terms: 7 + -14x + 2x2 = 0 Solving 7 + -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'. 3.5 + -7x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -7x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -7x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -7x + x2 = 0 + -3.5 -7x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -7x + x2 = -3.5 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 = -3.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -3.5 + 12.25 Combine like terms: -3.5 + 12.25 = 8.75 12.25 + -7x + x2 = 8.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -3.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -3.5 = 2.958039892 Simplifying x + -3.5 = 2.958039892 Reorder the terms: -3.5 + x = 2.958039892 Solving -3.5 + x = 2.958039892 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 = 2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.958039892 + 3.5 x = 2.958039892 + 3.5 Combine like terms: 2.958039892 + 3.5 = 6.458039892 x = 6.458039892 Simplifying x = 6.458039892Subproblem 2
x + -3.5 = -2.958039892 Simplifying x + -3.5 = -2.958039892 Reorder the terms: -3.5 + x = -2.958039892 Solving -3.5 + x = -2.958039892 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 = -2.958039892 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.958039892 + 3.5 x = -2.958039892 + 3.5 Combine like terms: -2.958039892 + 3.5 = 0.541960108 x = 0.541960108 Simplifying x = 0.541960108Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.458039892, 0.541960108}
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