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Simplifying 4x2 + -26x + -46 = 0 Reorder the terms: -46 + -26x + 4x2 = 0 Solving -46 + -26x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + -13x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying -23 + -13x + 2x2 = 0 Solving -23 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -6.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -6.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -6.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -6.5x + x2 = 0 + 11.5 -6.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -6.5x + x2 = 11.5 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 11.5 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 11.5 + 10.5625 Combine like terms: 11.5 + 10.5625 = 22.0625 10.5625 + -6.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -3.25) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -3.25 = 4.697073557 Simplifying x + -3.25 = 4.697073557 Reorder the terms: -3.25 + x = 4.697073557 Solving -3.25 + x = 4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.697073557 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.697073557 + 3.25 x = 4.697073557 + 3.25 Combine like terms: 4.697073557 + 3.25 = 7.947073557 x = 7.947073557 Simplifying x = 7.947073557Subproblem 2
x + -3.25 = -4.697073557 Simplifying x + -3.25 = -4.697073557 Reorder the terms: -3.25 + x = -4.697073557 Solving -3.25 + x = -4.697073557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.697073557 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.697073557 + 3.25 x = -4.697073557 + 3.25 Combine like terms: -4.697073557 + 3.25 = -1.447073557 x = -1.447073557 Simplifying x = -1.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.947073557, -1.447073557}Solution
x = {7.947073557, -1.447073557}
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