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Simplifying 9x2 + -170x + 578 = 0 Reorder the terms: 578 + -170x + 9x2 = 0 Solving 578 + -170x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 64.22222222 + -18.88888889x + x2 = 0 Move the constant term to the right: Add '-64.22222222' to each side of the equation. 64.22222222 + -18.88888889x + -64.22222222 + x2 = 0 + -64.22222222 Reorder the terms: 64.22222222 + -64.22222222 + -18.88888889x + x2 = 0 + -64.22222222 Combine like terms: 64.22222222 + -64.22222222 = 0.00000000 0.00000000 + -18.88888889x + x2 = 0 + -64.22222222 -18.88888889x + x2 = 0 + -64.22222222 Combine like terms: 0 + -64.22222222 = -64.22222222 -18.88888889x + x2 = -64.22222222 The x term is -18.88888889x. Take half its coefficient (-9.444444445). Square it (89.19753087) and add it to both sides. Add '89.19753087' to each side of the equation. -18.88888889x + 89.19753087 + x2 = -64.22222222 + 89.19753087 Reorder the terms: 89.19753087 + -18.88888889x + x2 = -64.22222222 + 89.19753087 Combine like terms: -64.22222222 + 89.19753087 = 24.97530865 89.19753087 + -18.88888889x + x2 = 24.97530865 Factor a perfect square on the left side: (x + -9.444444445)(x + -9.444444445) = 24.97530865 Calculate the square root of the right side: 4.997530255 Break this problem into two subproblems by setting (x + -9.444444445) equal to 4.997530255 and -4.997530255.Subproblem 1
x + -9.444444445 = 4.997530255 Simplifying x + -9.444444445 = 4.997530255 Reorder the terms: -9.444444445 + x = 4.997530255 Solving -9.444444445 + x = 4.997530255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.444444445' to each side of the equation. -9.444444445 + 9.444444445 + x = 4.997530255 + 9.444444445 Combine like terms: -9.444444445 + 9.444444445 = 0.000000000 0.000000000 + x = 4.997530255 + 9.444444445 x = 4.997530255 + 9.444444445 Combine like terms: 4.997530255 + 9.444444445 = 14.4419747 x = 14.4419747 Simplifying x = 14.4419747Subproblem 2
x + -9.444444445 = -4.997530255 Simplifying x + -9.444444445 = -4.997530255 Reorder the terms: -9.444444445 + x = -4.997530255 Solving -9.444444445 + x = -4.997530255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.444444445' to each side of the equation. -9.444444445 + 9.444444445 + x = -4.997530255 + 9.444444445 Combine like terms: -9.444444445 + 9.444444445 = 0.000000000 0.000000000 + x = -4.997530255 + 9.444444445 x = -4.997530255 + 9.444444445 Combine like terms: -4.997530255 + 9.444444445 = 4.44691419 x = 4.44691419 Simplifying x = 4.44691419Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.4419747, 4.44691419}
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