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Simplifying 4X2 + 56X + 1 = 0 Reorder the terms: 1 + 56X + 4X2 = 0 Solving 1 + 56X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 14X + X2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 14X + -0.25 + X2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 14X + X2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 14X + X2 = 0 + -0.25 14X + X2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 14X + X2 = -0.25 The X term is 14X. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14X + 49 + X2 = -0.25 + 49 Reorder the terms: 49 + 14X + X2 = -0.25 + 49 Combine like terms: -0.25 + 49 = 48.75 49 + 14X + X2 = 48.75 Factor a perfect square on the left side: (X + 7)(X + 7) = 48.75 Calculate the square root of the right side: 6.982120022 Break this problem into two subproblems by setting (X + 7) equal to 6.982120022 and -6.982120022.Subproblem 1
X + 7 = 6.982120022 Simplifying X + 7 = 6.982120022 Reorder the terms: 7 + X = 6.982120022 Solving 7 + X = 6.982120022 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = 6.982120022 + -7 Combine like terms: 7 + -7 = 0 0 + X = 6.982120022 + -7 X = 6.982120022 + -7 Combine like terms: 6.982120022 + -7 = -0.017879978 X = -0.017879978 Simplifying X = -0.017879978Subproblem 2
X + 7 = -6.982120022 Simplifying X + 7 = -6.982120022 Reorder the terms: 7 + X = -6.982120022 Solving 7 + X = -6.982120022 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = -6.982120022 + -7 Combine like terms: 7 + -7 = 0 0 + X = -6.982120022 + -7 X = -6.982120022 + -7 Combine like terms: -6.982120022 + -7 = -13.982120022 X = -13.982120022 Simplifying X = -13.982120022Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.017879978, -13.982120022}
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