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Simplifying -2x2 + -20x + -23 = 0 Reorder the terms: -23 + -20x + -2x2 = 0 Solving -23 + -20x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 20x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying 23 + 20x + 2x2 = 0 Solving 23 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 10x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 10x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 10x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 10x + x2 = 0 + -11.5 10x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 10x + x2 = -11.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -11.5 + 25 Reorder the terms: 25 + 10x + x2 = -11.5 + 25 Combine like terms: -11.5 + 25 = 13.5 25 + 10x + x2 = 13.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + 5) equal to 3.674234614 and -3.674234614.Subproblem 1
x + 5 = 3.674234614 Simplifying x + 5 = 3.674234614 Reorder the terms: 5 + x = 3.674234614 Solving 5 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 3.674234614 + -5 Combine like terms: 5 + -5 = 0 0 + x = 3.674234614 + -5 x = 3.674234614 + -5 Combine like terms: 3.674234614 + -5 = -1.325765386 x = -1.325765386 Simplifying x = -1.325765386Subproblem 2
x + 5 = -3.674234614 Simplifying x + 5 = -3.674234614 Reorder the terms: 5 + x = -3.674234614 Solving 5 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -3.674234614 + -5 Combine like terms: 5 + -5 = 0 0 + x = -3.674234614 + -5 x = -3.674234614 + -5 Combine like terms: -3.674234614 + -5 = -8.674234614 x = -8.674234614 Simplifying x = -8.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.325765386, -8.674234614}Solution
x = {-1.325765386, -8.674234614}
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