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Simplifying (2)(x)(x) + 20x = 25 Multiply x * x 2x2 + 20x = 25 Reorder the terms: 20x + 2x2 = 25 Solving 20x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 20x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 10x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 10x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 10x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 10x + x2 = 0 + 12.5 10x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 10x + x2 = 12.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 12.5 + 25 Reorder the terms: 25 + 10x + x2 = 12.5 + 25 Combine like terms: 12.5 + 25 = 37.5 25 + 10x + x2 = 37.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 37.5 Calculate the square root of the right side: 6.123724357 Break this problem into two subproblems by setting (x + 5) equal to 6.123724357 and -6.123724357.Subproblem 1
x + 5 = 6.123724357 Simplifying x + 5 = 6.123724357 Reorder the terms: 5 + x = 6.123724357 Solving 5 + x = 6.123724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.123724357 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.123724357 + -5 x = 6.123724357 + -5 Combine like terms: 6.123724357 + -5 = 1.123724357 x = 1.123724357 Simplifying x = 1.123724357Subproblem 2
x + 5 = -6.123724357 Simplifying x + 5 = -6.123724357 Reorder the terms: 5 + x = -6.123724357 Solving 5 + x = -6.123724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.123724357 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.123724357 + -5 x = -6.123724357 + -5 Combine like terms: -6.123724357 + -5 = -11.123724357 x = -11.123724357 Simplifying x = -11.123724357Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.123724357, -11.123724357}
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