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Simplifying 0 = 5x2 + -20x + 17 Reorder the terms: 0 = 17 + -20x + 5x2 Solving 0 = 17 + -20x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + 20x + -5x2 = 17 + -20x + 5x2 + -17 + 20x + -5x2 Reorder the terms: -17 + 20x + -5x2 = 17 + -17 + -20x + 20x + 5x2 + -5x2 Combine like terms: 17 + -17 = 0 -17 + 20x + -5x2 = 0 + -20x + 20x + 5x2 + -5x2 -17 + 20x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -17 + 20x + -5x2 = 0 + 5x2 + -5x2 -17 + 20x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -17 + 20x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.4 + -4x + x2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + -4x + -3.4 + x2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + -4x + x2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + -4x + x2 = 0 + -3.4 -4x + x2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 -4x + x2 = -3.4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.4 + 4 Reorder the terms: 4 + -4x + x2 = -3.4 + 4 Combine like terms: -3.4 + 4 = 0.6 4 + -4x + x2 = 0.6 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + -2) equal to 0.774596669 and -0.774596669.Subproblem 1
x + -2 = 0.774596669 Simplifying x + -2 = 0.774596669 Reorder the terms: -2 + x = 0.774596669 Solving -2 + x = 0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.774596669 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.774596669 + 2 x = 0.774596669 + 2 Combine like terms: 0.774596669 + 2 = 2.774596669 x = 2.774596669 Simplifying x = 2.774596669Subproblem 2
x + -2 = -0.774596669 Simplifying x + -2 = -0.774596669 Reorder the terms: -2 + x = -0.774596669 Solving -2 + x = -0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.774596669 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.774596669 + 2 x = -0.774596669 + 2 Combine like terms: -0.774596669 + 2 = 1.225403331 x = 1.225403331 Simplifying x = 1.225403331Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.774596669, 1.225403331}
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