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Simplifying 2x2 + -20x = -23 Reorder the terms: -20x + 2x2 = -23 Solving -20x + 2x2 = -23 Solving for variable 'x'. Reorder the terms: 23 + -20x + 2x2 = -23 + 23 Combine like terms: -23 + 23 = 0 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 = 8.674234614 x = 8.674234614 Simplifying x = 8.674234614Subproblem 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 = 1.325765386 x = 1.325765386 Simplifying x = 1.325765386Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.674234614, 1.325765386}
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