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Simplifying 56x2 + -616x + -12 = 0 Reorder the terms: -12 + -616x + 56x2 = 0 Solving -12 + -616x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -154x + 14x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -154x + 14x2)' equal to zero and attempt to solve: Simplifying -3 + -154x + 14x2 = 0 Solving -3 + -154x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + -11x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + -11x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + -11x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + -11x + x2 = 0 + 0.2142857143 -11x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 -11x + x2 = 0.2142857143 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 0.2142857143 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 0.2142857143 + 30.25 Combine like terms: 0.2142857143 + 30.25 = 30.4642857143 30.25 + -11x + x2 = 30.4642857143 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 30.4642857143 Calculate the square root of the right side: 5.519446142 Break this problem into two subproblems by setting (x + -5.5) equal to 5.519446142 and -5.519446142.Subproblem 1
x + -5.5 = 5.519446142 Simplifying x + -5.5 = 5.519446142 Reorder the terms: -5.5 + x = 5.519446142 Solving -5.5 + x = 5.519446142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.519446142 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.519446142 + 5.5 x = 5.519446142 + 5.5 Combine like terms: 5.519446142 + 5.5 = 11.019446142 x = 11.019446142 Simplifying x = 11.019446142Subproblem 2
x + -5.5 = -5.519446142 Simplifying x + -5.5 = -5.519446142 Reorder the terms: -5.5 + x = -5.519446142 Solving -5.5 + x = -5.519446142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.519446142 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.519446142 + 5.5 x = -5.519446142 + 5.5 Combine like terms: -5.519446142 + 5.5 = -0.019446142 x = -0.019446142 Simplifying x = -0.019446142Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.019446142, -0.019446142}Solution
x = {11.019446142, -0.019446142}
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