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Simplifying 4x2 + 112x + -224 = 0 Reorder the terms: -224 + 112x + 4x2 = 0 Solving -224 + 112x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-56 + 28x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-56 + 28x + x2)' equal to zero and attempt to solve: Simplifying -56 + 28x + x2 = 0 Solving -56 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 28x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 28x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 28x + x2 = 0 + 56 28x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 28x + x2 = 56 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 56 + 196 Reorder the terms: 196 + 28x + x2 = 56 + 196 Combine like terms: 56 + 196 = 252 196 + 28x + x2 = 252 Factor a perfect square on the left side: (x + 14)(x + 14) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + 14) equal to 15.874507866 and -15.874507866.Subproblem 1
x + 14 = 15.874507866 Simplifying x + 14 = 15.874507866 Reorder the terms: 14 + x = 15.874507866 Solving 14 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 15.874507866 + -14 Combine like terms: 14 + -14 = 0 0 + x = 15.874507866 + -14 x = 15.874507866 + -14 Combine like terms: 15.874507866 + -14 = 1.874507866 x = 1.874507866 Simplifying x = 1.874507866Subproblem 2
x + 14 = -15.874507866 Simplifying x + 14 = -15.874507866 Reorder the terms: 14 + x = -15.874507866 Solving 14 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -15.874507866 + -14 Combine like terms: 14 + -14 = 0 0 + x = -15.874507866 + -14 x = -15.874507866 + -14 Combine like terms: -15.874507866 + -14 = -29.874507866 x = -29.874507866 Simplifying x = -29.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.874507866, -29.874507866}Solution
x = {1.874507866, -29.874507866}
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