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Simplifying 2x2 + 14x + -216 = 0 Reorder the terms: -216 + 14x + 2x2 = 0 Solving -216 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-108 + 7x + x2)' equal to zero and attempt to solve: Simplifying -108 + 7x + x2 = 0 Solving -108 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 7x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 7x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 7x + x2 = 0 + 108 7x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 7x + x2 = 108 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 = 108 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 108 + 12.25 Combine like terms: 108 + 12.25 = 120.25 12.25 + 7x + x2 = 120.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 3.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 3.5 = 10.9658561 Simplifying x + 3.5 = 10.9658561 Reorder the terms: 3.5 + x = 10.9658561 Solving 3.5 + x = 10.9658561 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 = 10.9658561 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.9658561 + -3.5 x = 10.9658561 + -3.5 Combine like terms: 10.9658561 + -3.5 = 7.4658561 x = 7.4658561 Simplifying x = 7.4658561Subproblem 2
x + 3.5 = -10.9658561 Simplifying x + 3.5 = -10.9658561 Reorder the terms: 3.5 + x = -10.9658561 Solving 3.5 + x = -10.9658561 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 = -10.9658561 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.9658561 + -3.5 x = -10.9658561 + -3.5 Combine like terms: -10.9658561 + -3.5 = -14.4658561 x = -14.4658561 Simplifying x = -14.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.4658561, -14.4658561}Solution
x = {7.4658561, -14.4658561}
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