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Simplifying 2x2 + -10x + -23 = 0 Reorder the terms: -23 + -10x + 2x2 = 0 Solving -23 + -10x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -5x + x2 = 0 + 11.5 -5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -5x + x2 = 11.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 11.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 11.5 + 6.25 Combine like terms: 11.5 + 6.25 = 17.75 6.25 + -5x + x2 = 17.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + -2.5) equal to 4.213074887 and -4.213074887.Subproblem 1
x + -2.5 = 4.213074887 Simplifying x + -2.5 = 4.213074887 Reorder the terms: -2.5 + x = 4.213074887 Solving -2.5 + x = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.213074887 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.213074887 + 2.5 x = 4.213074887 + 2.5 Combine like terms: 4.213074887 + 2.5 = 6.713074887 x = 6.713074887 Simplifying x = 6.713074887Subproblem 2
x + -2.5 = -4.213074887 Simplifying x + -2.5 = -4.213074887 Reorder the terms: -2.5 + x = -4.213074887 Solving -2.5 + x = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.213074887 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.213074887 + 2.5 x = -4.213074887 + 2.5 Combine like terms: -4.213074887 + 2.5 = -1.713074887 x = -1.713074887 Simplifying x = -1.713074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.713074887, -1.713074887}
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