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Simplifying 2x(x + 7) = 13 Reorder the terms: 2x(7 + x) = 13 (7 * 2x + x * 2x) = 13 (14x + 2x2) = 13 Solving 14x + 2x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 14x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 14x + 2x2 = 0 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 = 0.830127019 x = 0.830127019 Simplifying x = 0.830127019Subproblem 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 = -7.830127019 x = -7.830127019 Simplifying x = -7.830127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.830127019, -7.830127019}
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