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Simplifying 20x + 3 = 4x2 Reorder the terms: 3 + 20x = 4x2 Solving 3 + 20x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 3 + 20x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.75 + -5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -5x + x2 = 0 + 0.75 -5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -5x + x2 = 0.75 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 = 0.75 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.75 + 6.25 Combine like terms: 0.75 + 6.25 = 7 6.25 + -5x + x2 = 7 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -2.5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -2.5 = 2.645751311 Simplifying x + -2.5 = 2.645751311 Reorder the terms: -2.5 + x = 2.645751311 Solving -2.5 + x = 2.645751311 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 = 2.645751311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.645751311 + 2.5 x = 2.645751311 + 2.5 Combine like terms: 2.645751311 + 2.5 = 5.145751311 x = 5.145751311 Simplifying x = 5.145751311Subproblem 2
x + -2.5 = -2.645751311 Simplifying x + -2.5 = -2.645751311 Reorder the terms: -2.5 + x = -2.645751311 Solving -2.5 + x = -2.645751311 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 = -2.645751311 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.645751311 + 2.5 x = -2.645751311 + 2.5 Combine like terms: -2.645751311 + 2.5 = -0.145751311 x = -0.145751311 Simplifying x = -0.145751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.145751311, -0.145751311}
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