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Simplifying 4x2 + -20x + -69 = 0 Reorder the terms: -69 + -20x + 4x2 = 0 Solving -69 + -20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + -5x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + -5x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + -5x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + -5x + x2 = 0 + 17.25 -5x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 -5x + x2 = 17.25 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 = 17.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 17.25 + 6.25 Combine like terms: 17.25 + 6.25 = 23.5 6.25 + -5x + x2 = 23.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + -2.5) equal to 4.847679857 and -4.847679857.Subproblem 1
x + -2.5 = 4.847679857 Simplifying x + -2.5 = 4.847679857 Reorder the terms: -2.5 + x = 4.847679857 Solving -2.5 + x = 4.847679857 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 = 4.847679857 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.847679857 + 2.5 x = 4.847679857 + 2.5 Combine like terms: 4.847679857 + 2.5 = 7.347679857 x = 7.347679857 Simplifying x = 7.347679857Subproblem 2
x + -2.5 = -4.847679857 Simplifying x + -2.5 = -4.847679857 Reorder the terms: -2.5 + x = -4.847679857 Solving -2.5 + x = -4.847679857 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 = -4.847679857 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.847679857 + 2.5 x = -4.847679857 + 2.5 Combine like terms: -4.847679857 + 2.5 = -2.347679857 x = -2.347679857 Simplifying x = -2.347679857Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.347679857, -2.347679857}
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