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Simplifying 2x2 + 14x + -212 = 0 Reorder the terms: -212 + 14x + 2x2 = 0 Solving -212 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-106 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-106 + 7x + x2)' equal to zero and attempt to solve: Simplifying -106 + 7x + x2 = 0 Solving -106 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '106' to each side of the equation. -106 + 7x + 106 + x2 = 0 + 106 Reorder the terms: -106 + 106 + 7x + x2 = 0 + 106 Combine like terms: -106 + 106 = 0 0 + 7x + x2 = 0 + 106 7x + x2 = 0 + 106 Combine like terms: 0 + 106 = 106 7x + x2 = 106 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 = 106 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 106 + 12.25 Combine like terms: 106 + 12.25 = 118.25 12.25 + 7x + x2 = 118.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 118.25 Calculate the square root of the right side: 10.874281585 Break this problem into two subproblems by setting (x + 3.5) equal to 10.874281585 and -10.874281585.Subproblem 1
x + 3.5 = 10.874281585 Simplifying x + 3.5 = 10.874281585 Reorder the terms: 3.5 + x = 10.874281585 Solving 3.5 + x = 10.874281585 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 = 10.874281585 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.874281585 + -3.5 x = 10.874281585 + -3.5 Combine like terms: 10.874281585 + -3.5 = 7.374281585 x = 7.374281585 Simplifying x = 7.374281585Subproblem 2
x + 3.5 = -10.874281585 Simplifying x + 3.5 = -10.874281585 Reorder the terms: 3.5 + x = -10.874281585 Solving 3.5 + x = -10.874281585 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 = -10.874281585 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.874281585 + -3.5 x = -10.874281585 + -3.5 Combine like terms: -10.874281585 + -3.5 = -14.374281585 x = -14.374281585 Simplifying x = -14.374281585Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.374281585, -14.374281585}Solution
x = {7.374281585, -14.374281585}
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