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Simplifying 4x2 + 56x + -14 = 0 Reorder the terms: -14 + 56x + 4x2 = 0 Solving -14 + 56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 28x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 28x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 28x + 2x2 = 0 Solving -7 + 28x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 14x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 14x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 14x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 14x + x2 = 0 + 3.5 14x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 14x + x2 = 3.5 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 = 3.5 + 49 Reorder the terms: 49 + 14x + x2 = 3.5 + 49 Combine like terms: 3.5 + 49 = 52.5 49 + 14x + x2 = 52.5 Factor a perfect square on the left side: (x + 7)(x + 7) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + 7) equal to 7.245688373 and -7.245688373.Subproblem 1
x + 7 = 7.245688373 Simplifying x + 7 = 7.245688373 Reorder the terms: 7 + x = 7.245688373 Solving 7 + x = 7.245688373 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 = 7.245688373 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.245688373 + -7 x = 7.245688373 + -7 Combine like terms: 7.245688373 + -7 = 0.245688373 x = 0.245688373 Simplifying x = 0.245688373Subproblem 2
x + 7 = -7.245688373 Simplifying x + 7 = -7.245688373 Reorder the terms: 7 + x = -7.245688373 Solving 7 + x = -7.245688373 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 = -7.245688373 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.245688373 + -7 x = -7.245688373 + -7 Combine like terms: -7.245688373 + -7 = -14.245688373 x = -14.245688373 Simplifying x = -14.245688373Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.245688373, -14.245688373}Solution
x = {0.245688373, -14.245688373}
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