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Simplifying -4x2 + -26x + -4 = 0 Reorder the terms: -4 + -26x + -4x2 = 0 Solving -4 + -26x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(2 + 13x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + 13x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + 13x + 2x2 = 0 Solving 2 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 6.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 6.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 6.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6.5x + x2 = 0 + -1 6.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 6.5x + x2 = -1 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 = -1 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -1 + 10.5625 Combine like terms: -1 + 10.5625 = 9.5625 10.5625 + 6.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + 3.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + 3.25 = 3.092329219 Simplifying x + 3.25 = 3.092329219 Reorder the terms: 3.25 + x = 3.092329219 Solving 3.25 + x = 3.092329219 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 = 3.092329219 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.092329219 + -3.25 x = 3.092329219 + -3.25 Combine like terms: 3.092329219 + -3.25 = -0.157670781 x = -0.157670781 Simplifying x = -0.157670781Subproblem 2
x + 3.25 = -3.092329219 Simplifying x + 3.25 = -3.092329219 Reorder the terms: 3.25 + x = -3.092329219 Solving 3.25 + x = -3.092329219 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 = -3.092329219 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.092329219 + -3.25 x = -3.092329219 + -3.25 Combine like terms: -3.092329219 + -3.25 = -6.342329219 x = -6.342329219 Simplifying x = -6.342329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.157670781, -6.342329219}Solution
x = {-0.157670781, -6.342329219}
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