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Simplifying 36x = 4x2 + -5 Reorder the terms: 36x = -5 + 4x2 Solving 36x = -5 + 4x2 Solving for variable 'x'. Reorder the terms: 5 + 36x + -4x2 = -5 + 4x2 + 5 + -4x2 Reorder the terms: 5 + 36x + -4x2 = -5 + 5 + 4x2 + -4x2 Combine like terms: -5 + 5 = 0 5 + 36x + -4x2 = 0 + 4x2 + -4x2 5 + 36x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + 36x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -9x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -9x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -9x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -9x + x2 = 0 + 1.25 -9x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -9x + x2 = 1.25 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 1.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 1.25 + 20.25 Combine like terms: 1.25 + 20.25 = 21.5 20.25 + -9x + x2 = 21.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + -4.5) equal to 4.636809248 and -4.636809248.Subproblem 1
x + -4.5 = 4.636809248 Simplifying x + -4.5 = 4.636809248 Reorder the terms: -4.5 + x = 4.636809248 Solving -4.5 + x = 4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.636809248 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.636809248 + 4.5 x = 4.636809248 + 4.5 Combine like terms: 4.636809248 + 4.5 = 9.136809248 x = 9.136809248 Simplifying x = 9.136809248Subproblem 2
x + -4.5 = -4.636809248 Simplifying x + -4.5 = -4.636809248 Reorder the terms: -4.5 + x = -4.636809248 Solving -4.5 + x = -4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.636809248 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.636809248 + 4.5 x = -4.636809248 + 4.5 Combine like terms: -4.636809248 + 4.5 = -0.136809248 x = -0.136809248 Simplifying x = -0.136809248Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.136809248, -0.136809248}
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