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Simplifying 2x2 + -10x + -20 = 9 Reorder the terms: -20 + -10x + 2x2 = 9 Solving -20 + -10x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -20 + -9 + -10x + 2x2 = 9 + -9 Combine like terms: -20 + -9 = -29 -29 + -10x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -29 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + -5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -5x + x2 = 0 + 14.5 -5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -5x + x2 = 14.5 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 = 14.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 14.5 + 6.25 Combine like terms: 14.5 + 6.25 = 20.75 6.25 + -5x + x2 = 20.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 20.75 Calculate the square root of the right side: 4.55521679 Break this problem into two subproblems by setting (x + -2.5) equal to 4.55521679 and -4.55521679.Subproblem 1
x + -2.5 = 4.55521679 Simplifying x + -2.5 = 4.55521679 Reorder the terms: -2.5 + x = 4.55521679 Solving -2.5 + x = 4.55521679 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 = 4.55521679 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.55521679 + 2.5 x = 4.55521679 + 2.5 Combine like terms: 4.55521679 + 2.5 = 7.05521679 x = 7.05521679 Simplifying x = 7.05521679Subproblem 2
x + -2.5 = -4.55521679 Simplifying x + -2.5 = -4.55521679 Reorder the terms: -2.5 + x = -4.55521679 Solving -2.5 + x = -4.55521679 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 = -4.55521679 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.55521679 + 2.5 x = -4.55521679 + 2.5 Combine like terms: -4.55521679 + 2.5 = -2.05521679 x = -2.05521679 Simplifying x = -2.05521679Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.05521679, -2.05521679}
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