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Simplifying 36x2 + -60x = -17 Reorder the terms: -60x + 36x2 = -17 Solving -60x + 36x2 = -17 Solving for variable 'x'. Reorder the terms: 17 + -60x + 36x2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + -60x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.4722222222 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '-0.4722222222' to each side of the equation. 0.4722222222 + -1.666666667x + -0.4722222222 + x2 = 0 + -0.4722222222 Reorder the terms: 0.4722222222 + -0.4722222222 + -1.666666667x + x2 = 0 + -0.4722222222 Combine like terms: 0.4722222222 + -0.4722222222 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + -0.4722222222 -1.666666667x + x2 = 0 + -0.4722222222 Combine like terms: 0 + -0.4722222222 = -0.4722222222 -1.666666667x + x2 = -0.4722222222 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = -0.4722222222 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = -0.4722222222 + 0.6944444447 Combine like terms: -0.4722222222 + 0.6944444447 = 0.2222222225 0.6944444447 + -1.666666667x + x2 = 0.2222222225 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 0.2222222225 Calculate the square root of the right side: 0.471404521 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 0.471404521 and -0.471404521.Subproblem 1
x + -0.8333333335 = 0.471404521 Simplifying x + -0.8333333335 = 0.471404521 Reorder the terms: -0.8333333335 + x = 0.471404521 Solving -0.8333333335 + x = 0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 0.471404521 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 0.471404521 + 0.8333333335 x = 0.471404521 + 0.8333333335 Combine like terms: 0.471404521 + 0.8333333335 = 1.3047378545 x = 1.3047378545 Simplifying x = 1.3047378545Subproblem 2
x + -0.8333333335 = -0.471404521 Simplifying x + -0.8333333335 = -0.471404521 Reorder the terms: -0.8333333335 + x = -0.471404521 Solving -0.8333333335 + x = -0.471404521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -0.471404521 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -0.471404521 + 0.8333333335 x = -0.471404521 + 0.8333333335 Combine like terms: -0.471404521 + 0.8333333335 = 0.3619288125 x = 0.3619288125 Simplifying x = 0.3619288125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3047378545, 0.3619288125}
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