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Simplifying 4x2 = 36x + 9 Reorder the terms: 4x2 = 9 + 36x Solving 4x2 = 9 + 36x Solving for variable 'x'. Reorder the terms: -9 + -36x + 4x2 = 9 + 36x + -9 + -36x Reorder the terms: -9 + -36x + 4x2 = 9 + -9 + 36x + -36x Combine like terms: 9 + -9 = 0 -9 + -36x + 4x2 = 0 + 36x + -36x -9 + -36x + 4x2 = 36x + -36x Combine like terms: 36x + -36x = 0 -9 + -36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -9x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -9x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -9x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -9x + x2 = 0 + 2.25 -9x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -9x + x2 = 2.25 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 = 2.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 2.25 + 20.25 Combine like terms: 2.25 + 20.25 = 22.5 20.25 + -9x + x2 = 22.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -4.5) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -4.5 = 4.74341649 Simplifying x + -4.5 = 4.74341649 Reorder the terms: -4.5 + x = 4.74341649 Solving -4.5 + x = 4.74341649 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 = 4.74341649 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.74341649 + 4.5 x = 4.74341649 + 4.5 Combine like terms: 4.74341649 + 4.5 = 9.24341649 x = 9.24341649 Simplifying x = 9.24341649Subproblem 2
x + -4.5 = -4.74341649 Simplifying x + -4.5 = -4.74341649 Reorder the terms: -4.5 + x = -4.74341649 Solving -4.5 + x = -4.74341649 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 = -4.74341649 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.74341649 + 4.5 x = -4.74341649 + 4.5 Combine like terms: -4.74341649 + 4.5 = -0.24341649 x = -0.24341649 Simplifying x = -0.24341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.24341649, -0.24341649}
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