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Simplifying 4x2 + -44x + -70 = 0 Reorder the terms: -70 + -44x + 4x2 = 0 Solving -70 + -44x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -22x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -22x + 2x2)' equal to zero and attempt to solve: Simplifying -35 + -22x + 2x2 = 0 Solving -35 + -22x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -11x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -11x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -11x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -11x + x2 = 0 + 17.5 -11x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -11x + x2 = 17.5 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 = 17.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 17.5 + 30.25 Combine like terms: 17.5 + 30.25 = 47.75 30.25 + -11x + x2 = 47.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 47.75 Calculate the square root of the right side: 6.910137481 Break this problem into two subproblems by setting (x + -5.5) equal to 6.910137481 and -6.910137481.Subproblem 1
x + -5.5 = 6.910137481 Simplifying x + -5.5 = 6.910137481 Reorder the terms: -5.5 + x = 6.910137481 Solving -5.5 + x = 6.910137481 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 = 6.910137481 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.910137481 + 5.5 x = 6.910137481 + 5.5 Combine like terms: 6.910137481 + 5.5 = 12.410137481 x = 12.410137481 Simplifying x = 12.410137481Subproblem 2
x + -5.5 = -6.910137481 Simplifying x + -5.5 = -6.910137481 Reorder the terms: -5.5 + x = -6.910137481 Solving -5.5 + x = -6.910137481 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 = -6.910137481 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.910137481 + 5.5 x = -6.910137481 + 5.5 Combine like terms: -6.910137481 + 5.5 = -1.410137481 x = -1.410137481 Simplifying x = -1.410137481Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.410137481, -1.410137481}Solution
x = {12.410137481, -1.410137481}
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