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Simplifying 9x2 + -144x + 64 = 0 Reorder the terms: 64 + -144x + 9x2 = 0 Solving 64 + -144x + 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'. 7.111111111 + -16x + x2 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + -16x + -7.111111111 + x2 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + -16x + x2 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + -16x + x2 = 0 + -7.111111111 -16x + x2 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 -16x + x2 = -7.111111111 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -7.111111111 + 64 Reorder the terms: 64 + -16x + x2 = -7.111111111 + 64 Combine like terms: -7.111111111 + 64 = 56.888888889 64 + -16x + x2 = 56.888888889 Factor a perfect square on the left side: (x + -8)(x + -8) = 56.888888889 Calculate the square root of the right side: 7.542472333 Break this problem into two subproblems by setting (x + -8) equal to 7.542472333 and -7.542472333.Subproblem 1
x + -8 = 7.542472333 Simplifying x + -8 = 7.542472333 Reorder the terms: -8 + x = 7.542472333 Solving -8 + x = 7.542472333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.542472333 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.542472333 + 8 x = 7.542472333 + 8 Combine like terms: 7.542472333 + 8 = 15.542472333 x = 15.542472333 Simplifying x = 15.542472333Subproblem 2
x + -8 = -7.542472333 Simplifying x + -8 = -7.542472333 Reorder the terms: -8 + x = -7.542472333 Solving -8 + x = -7.542472333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.542472333 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.542472333 + 8 x = -7.542472333 + 8 Combine like terms: -7.542472333 + 8 = 0.457527667 x = 0.457527667 Simplifying x = 0.457527667Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.542472333, 0.457527667}
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