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Simplifying 4x2 + 56x + -272 = 0 Reorder the terms: -272 + 56x + 4x2 = 0 Solving -272 + 56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-68 + 14x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-68 + 14x + x2)' equal to zero and attempt to solve: Simplifying -68 + 14x + x2 = 0 Solving -68 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 14x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 14x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 14x + x2 = 0 + 68 14x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 14x + x2 = 68 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 = 68 + 49 Reorder the terms: 49 + 14x + x2 = 68 + 49 Combine like terms: 68 + 49 = 117 49 + 14x + x2 = 117 Factor a perfect square on the left side: (x + 7)(x + 7) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 7) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 7 = 10.816653826 Simplifying x + 7 = 10.816653826 Reorder the terms: 7 + x = 10.816653826 Solving 7 + x = 10.816653826 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 = 10.816653826 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.816653826 + -7 x = 10.816653826 + -7 Combine like terms: 10.816653826 + -7 = 3.816653826 x = 3.816653826 Simplifying x = 3.816653826Subproblem 2
x + 7 = -10.816653826 Simplifying x + 7 = -10.816653826 Reorder the terms: 7 + x = -10.816653826 Solving 7 + x = -10.816653826 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 = -10.816653826 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.816653826 + -7 x = -10.816653826 + -7 Combine like terms: -10.816653826 + -7 = -17.816653826 x = -17.816653826 Simplifying x = -17.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.816653826, -17.816653826}Solution
x = {3.816653826, -17.816653826}
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