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Simplifying 0 = 9x2 + -1x + -32 Reorder the terms: 0 = -32 + -1x + 9x2 Solving 0 = -32 + -1x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 32 = 32 32 + x + -9x2 = -32 + -1x + 9x2 + 32 + x + -9x2 Reorder the terms: 32 + x + -9x2 = -32 + 32 + -1x + x + 9x2 + -9x2 Combine like terms: -32 + 32 = 0 32 + x + -9x2 = 0 + -1x + x + 9x2 + -9x2 32 + x + -9x2 = -1x + x + 9x2 + -9x2 Combine like terms: -1x + x = 0 32 + x + -9x2 = 0 + 9x2 + -9x2 32 + x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 32 + x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -3.555555556 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '3.555555556' to each side of the equation. -3.555555556 + -0.1111111111x + 3.555555556 + x2 = 0 + 3.555555556 Reorder the terms: -3.555555556 + 3.555555556 + -0.1111111111x + x2 = 0 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 3.555555556 -0.1111111111x + x2 = 0 + 3.555555556 Combine like terms: 0 + 3.555555556 = 3.555555556 -0.1111111111x + x2 = 3.555555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1111111111x + 0.25 + x2 = 3.555555556 + 0.25 Reorder the terms: 0.25 + -0.1111111111x + x2 = 3.555555556 + 0.25 Combine like terms: 3.555555556 + 0.25 = 3.805555556 0.25 + -0.1111111111x + x2 = 3.805555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.805555556 Calculate the square root of the right side: 1.950783319 Break this problem into two subproblems by setting (x + 0.5) equal to 1.950783319 and -1.950783319.Subproblem 1
x + 0.5 = 1.950783319 Simplifying x + 0.5 = 1.950783319 Reorder the terms: 0.5 + x = 1.950783319 Solving 0.5 + x = 1.950783319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.950783319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.950783319 + -0.5 x = 1.950783319 + -0.5 Combine like terms: 1.950783319 + -0.5 = 1.450783319 x = 1.450783319 Simplifying x = 1.450783319Subproblem 2
x + 0.5 = -1.950783319 Simplifying x + 0.5 = -1.950783319 Reorder the terms: 0.5 + x = -1.950783319 Solving 0.5 + x = -1.950783319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.950783319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.950783319 + -0.5 x = -1.950783319 + -0.5 Combine like terms: -1.950783319 + -0.5 = -2.450783319 x = -2.450783319 Simplifying x = -2.450783319Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.450783319, -2.450783319}
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