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Simplifying 0 = 9x2 + -64x + -25 Reorder the terms: 0 = -25 + -64x + 9x2 Solving 0 = -25 + -64x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 64x + -9x2 = -25 + -64x + 9x2 + 25 + 64x + -9x2 Reorder the terms: 25 + 64x + -9x2 = -25 + 25 + -64x + 64x + 9x2 + -9x2 Combine like terms: -25 + 25 = 0 25 + 64x + -9x2 = 0 + -64x + 64x + 9x2 + -9x2 25 + 64x + -9x2 = -64x + 64x + 9x2 + -9x2 Combine like terms: -64x + 64x = 0 25 + 64x + -9x2 = 0 + 9x2 + -9x2 25 + 64x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 25 + 64x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.777777778 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -7.111111111x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -7.111111111x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -7.111111111x + x2 = 0 + 2.777777778 -7.111111111x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -7.111111111x + x2 = 2.777777778 The x term is -7.111111111x. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111x + 12.64197531 + x2 = 2.777777778 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = 2.777777778 + 12.64197531 Combine like terms: 2.777777778 + 12.64197531 = 15.419753088 12.64197531 + -7.111111111x + x2 = 15.419753088 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 15.419753088 Calculate the square root of the right side: 3.926799344 Break this problem into two subproblems by setting (x + -3.555555556) equal to 3.926799344 and -3.926799344.Subproblem 1
x + -3.555555556 = 3.926799344 Simplifying x + -3.555555556 = 3.926799344 Reorder the terms: -3.555555556 + x = 3.926799344 Solving -3.555555556 + x = 3.926799344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = 3.926799344 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 3.926799344 + 3.555555556 x = 3.926799344 + 3.555555556 Combine like terms: 3.926799344 + 3.555555556 = 7.4823549 x = 7.4823549 Simplifying x = 7.4823549Subproblem 2
x + -3.555555556 = -3.926799344 Simplifying x + -3.555555556 = -3.926799344 Reorder the terms: -3.555555556 + x = -3.926799344 Solving -3.555555556 + x = -3.926799344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = -3.926799344 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -3.926799344 + 3.555555556 x = -3.926799344 + 3.555555556 Combine like terms: -3.926799344 + 3.555555556 = -0.371243788 x = -0.371243788 Simplifying x = -0.371243788Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.4823549, -0.371243788}
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