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Simplifying 9x2 + -72x + -5 = 0 Reorder the terms: -5 + -72x + 9x2 = 0 Solving -5 + -72x + 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'. -0.5555555556 + -8x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -8x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -8x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + 0.5555555556 -8x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -8x + x2 = 0.5555555556 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 0.5555555556 + 16 Reorder the terms: 16 + -8x + x2 = 0.5555555556 + 16 Combine like terms: 0.5555555556 + 16 = 16.5555555556 16 + -8x + x2 = 16.5555555556 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.5555555556 Calculate the square root of the right side: 4.068851872 Break this problem into two subproblems by setting (x + -4) equal to 4.068851872 and -4.068851872.Subproblem 1
x + -4 = 4.068851872 Simplifying x + -4 = 4.068851872 Reorder the terms: -4 + x = 4.068851872 Solving -4 + x = 4.068851872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.068851872 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.068851872 + 4 x = 4.068851872 + 4 Combine like terms: 4.068851872 + 4 = 8.068851872 x = 8.068851872 Simplifying x = 8.068851872Subproblem 2
x + -4 = -4.068851872 Simplifying x + -4 = -4.068851872 Reorder the terms: -4 + x = -4.068851872 Solving -4 + x = -4.068851872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.068851872 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.068851872 + 4 x = -4.068851872 + 4 Combine like terms: -4.068851872 + 4 = -0.068851872 x = -0.068851872 Simplifying x = -0.068851872Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.068851872, -0.068851872}
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