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Simplifying 4x2 = 20x + 9 Reorder the terms: 4x2 = 9 + 20x Solving 4x2 = 9 + 20x Solving for variable 'x'. Reorder the terms: -9 + -20x + 4x2 = 9 + 20x + -9 + -20x Reorder the terms: -9 + -20x + 4x2 = 9 + -9 + 20x + -20x Combine like terms: 9 + -9 = 0 -9 + -20x + 4x2 = 0 + 20x + -20x -9 + -20x + 4x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -9 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -5x + x2 = 0 + 2.25 -5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -5x + x2 = 2.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.25 + 6.25 Combine like terms: 2.25 + 6.25 = 8.5 6.25 + -5x + x2 = 8.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + -2.5) equal to 2.915475947 and -2.915475947.Subproblem 1
x + -2.5 = 2.915475947 Simplifying x + -2.5 = 2.915475947 Reorder the terms: -2.5 + x = 2.915475947 Solving -2.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.915475947 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.915475947 + 2.5 x = 2.915475947 + 2.5 Combine like terms: 2.915475947 + 2.5 = 5.415475947 x = 5.415475947 Simplifying x = 5.415475947Subproblem 2
x + -2.5 = -2.915475947 Simplifying x + -2.5 = -2.915475947 Reorder the terms: -2.5 + x = -2.915475947 Solving -2.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.915475947 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.915475947 + 2.5 x = -2.915475947 + 2.5 Combine like terms: -2.915475947 + 2.5 = -0.415475947 x = -0.415475947 Simplifying x = -0.415475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.415475947, -0.415475947}
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