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Simplifying 9x2 + -25x = 25x + -12 Reorder the terms: -25x + 9x2 = 25x + -12 Reorder the terms: -25x + 9x2 = -12 + 25x Solving -25x + 9x2 = -12 + 25x Solving for variable 'x'. Reorder the terms: 12 + -25x + -25x + 9x2 = -12 + 25x + 12 + -25x Combine like terms: -25x + -25x = -50x 12 + -50x + 9x2 = -12 + 25x + 12 + -25x Reorder the terms: 12 + -50x + 9x2 = -12 + 12 + 25x + -25x Combine like terms: -12 + 12 = 0 12 + -50x + 9x2 = 0 + 25x + -25x 12 + -50x + 9x2 = 25x + -25x Combine like terms: 25x + -25x = 0 12 + -50x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.333333333 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -5.555555556x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -5.555555556x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -5.555555556x + x2 = 0 + -1.333333333 -5.555555556x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -5.555555556x + x2 = -1.333333333 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = -1.333333333 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = -1.333333333 + 7.716049384 Combine like terms: -1.333333333 + 7.716049384 = 6.382716051 7.716049384 + -5.555555556x + x2 = 6.382716051 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 6.382716051 Calculate the square root of the right side: 2.526403778 Break this problem into two subproblems by setting (x + -2.777777778) equal to 2.526403778 and -2.526403778.Subproblem 1
x + -2.777777778 = 2.526403778 Simplifying x + -2.777777778 = 2.526403778 Reorder the terms: -2.777777778 + x = 2.526403778 Solving -2.777777778 + x = 2.526403778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 2.526403778 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 2.526403778 + 2.777777778 x = 2.526403778 + 2.777777778 Combine like terms: 2.526403778 + 2.777777778 = 5.304181556 x = 5.304181556 Simplifying x = 5.304181556Subproblem 2
x + -2.777777778 = -2.526403778 Simplifying x + -2.777777778 = -2.526403778 Reorder the terms: -2.777777778 + x = -2.526403778 Solving -2.777777778 + x = -2.526403778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -2.526403778 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -2.526403778 + 2.777777778 x = -2.526403778 + 2.777777778 Combine like terms: -2.526403778 + 2.777777778 = 0.251374 x = 0.251374 Simplifying x = 0.251374Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.304181556, 0.251374}
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