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Simplifying 17x2 + -120x + 180 = 0 Reorder the terms: 180 + -120x + 17x2 = 0 Solving 180 + -120x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 10.58823529 + -7.058823529x + x2 = 0 Move the constant term to the right: Add '-10.58823529' to each side of the equation. 10.58823529 + -7.058823529x + -10.58823529 + x2 = 0 + -10.58823529 Reorder the terms: 10.58823529 + -10.58823529 + -7.058823529x + x2 = 0 + -10.58823529 Combine like terms: 10.58823529 + -10.58823529 = 0.00000000 0.00000000 + -7.058823529x + x2 = 0 + -10.58823529 -7.058823529x + x2 = 0 + -10.58823529 Combine like terms: 0 + -10.58823529 = -10.58823529 -7.058823529x + x2 = -10.58823529 The x term is -7.058823529x. Take half its coefficient (-3.529411765). Square it (12.45674741) and add it to both sides. Add '12.45674741' to each side of the equation. -7.058823529x + 12.45674741 + x2 = -10.58823529 + 12.45674741 Reorder the terms: 12.45674741 + -7.058823529x + x2 = -10.58823529 + 12.45674741 Combine like terms: -10.58823529 + 12.45674741 = 1.86851212 12.45674741 + -7.058823529x + x2 = 1.86851212 Factor a perfect square on the left side: (x + -3.529411765)(x + -3.529411765) = 1.86851212 Calculate the square root of the right side: 1.366935302 Break this problem into two subproblems by setting (x + -3.529411765) equal to 1.366935302 and -1.366935302.Subproblem 1
x + -3.529411765 = 1.366935302 Simplifying x + -3.529411765 = 1.366935302 Reorder the terms: -3.529411765 + x = 1.366935302 Solving -3.529411765 + x = 1.366935302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.529411765' to each side of the equation. -3.529411765 + 3.529411765 + x = 1.366935302 + 3.529411765 Combine like terms: -3.529411765 + 3.529411765 = 0.000000000 0.000000000 + x = 1.366935302 + 3.529411765 x = 1.366935302 + 3.529411765 Combine like terms: 1.366935302 + 3.529411765 = 4.896347067 x = 4.896347067 Simplifying x = 4.896347067Subproblem 2
x + -3.529411765 = -1.366935302 Simplifying x + -3.529411765 = -1.366935302 Reorder the terms: -3.529411765 + x = -1.366935302 Solving -3.529411765 + x = -1.366935302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.529411765' to each side of the equation. -3.529411765 + 3.529411765 + x = -1.366935302 + 3.529411765 Combine like terms: -3.529411765 + 3.529411765 = 0.000000000 0.000000000 + x = -1.366935302 + 3.529411765 x = -1.366935302 + 3.529411765 Combine like terms: -1.366935302 + 3.529411765 = 2.162476463 x = 2.162476463 Simplifying x = 2.162476463Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.896347067, 2.162476463}
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