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Simplifying 0 = 1x2 + 7x + 11 Reorder the terms: 0 = 11 + 7x + 1x2 Solving 0 = 11 + 7x + 1x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -7x + -1x2 = 11 + 7x + 1x2 + -11 + -7x + -1x2 Reorder the terms: -11 + -7x + -1x2 = 11 + -11 + 7x + -7x + 1x2 + -1x2 Combine like terms: 11 + -11 = 0 -11 + -7x + -1x2 = 0 + 7x + -7x + 1x2 + -1x2 -11 + -7x + -1x2 = 7x + -7x + 1x2 + -1x2 Combine like terms: 7x + -7x = 0 -11 + -7x + -1x2 = 0 + 1x2 + -1x2 -11 + -7x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -11 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 7x + x2)' equal to zero and attempt to solve: Simplifying 11 + 7x + x2 = 0 Solving 11 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 7x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 7x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 7x + x2 = 0 + -11 7x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 7x + x2 = -11 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 = -11 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -11 + 12.25 Combine like terms: -11 + 12.25 = 1.25 12.25 + 7x + x2 = 1.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 3.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 3.5 = 1.118033989 Simplifying x + 3.5 = 1.118033989 Reorder the terms: 3.5 + x = 1.118033989 Solving 3.5 + x = 1.118033989 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 = 1.118033989 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 1.118033989 + -3.5 x = 1.118033989 + -3.5 Combine like terms: 1.118033989 + -3.5 = -2.381966011 x = -2.381966011 Simplifying x = -2.381966011Subproblem 2
x + 3.5 = -1.118033989 Simplifying x + 3.5 = -1.118033989 Reorder the terms: 3.5 + x = -1.118033989 Solving 3.5 + x = -1.118033989 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 = -1.118033989 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -1.118033989 + -3.5 x = -1.118033989 + -3.5 Combine like terms: -1.118033989 + -3.5 = -4.618033989 x = -4.618033989 Simplifying x = -4.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.381966011, -4.618033989}Solution
x = {-2.381966011, -4.618033989}
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