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Simplifying 2x2 + -14x + -13 = 0 Reorder the terms: -13 + -14x + 2x2 = 0 Solving -13 + -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'. -6.5 + -7x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -7x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -7x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -7x + x2 = 0 + 6.5 -7x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -7x + x2 = 6.5 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 = 6.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 6.5 + 12.25 Combine like terms: 6.5 + 12.25 = 18.75 12.25 + -7x + x2 = 18.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + -3.5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + -3.5 = 4.330127019 Simplifying x + -3.5 = 4.330127019 Reorder the terms: -3.5 + x = 4.330127019 Solving -3.5 + x = 4.330127019 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 = 4.330127019 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.330127019 + 3.5 x = 4.330127019 + 3.5 Combine like terms: 4.330127019 + 3.5 = 7.830127019 x = 7.830127019 Simplifying x = 7.830127019Subproblem 2
x + -3.5 = -4.330127019 Simplifying x + -3.5 = -4.330127019 Reorder the terms: -3.5 + x = -4.330127019 Solving -3.5 + x = -4.330127019 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 = -4.330127019 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.330127019 + 3.5 x = -4.330127019 + 3.5 Combine like terms: -4.330127019 + 3.5 = -0.830127019 x = -0.830127019 Simplifying x = -0.830127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.830127019, -0.830127019}
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