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Simplifying 395 = 4x(x + -20) Reorder the terms: 395 = 4x(-20 + x) 395 = (-20 * 4x + x * 4x) 395 = (-80x + 4x2) Solving 395 = -80x + 4x2 Solving for variable 'x'. Reorder the terms: 395 + 80x + -4x2 = -80x + 80x + 4x2 + -4x2 Combine like terms: -80x + 80x = 0 395 + 80x + -4x2 = 0 + 4x2 + -4x2 395 + 80x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 395 + 80x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -98.75 + -20x + x2 = 0 Move the constant term to the right: Add '98.75' to each side of the equation. -98.75 + -20x + 98.75 + x2 = 0 + 98.75 Reorder the terms: -98.75 + 98.75 + -20x + x2 = 0 + 98.75 Combine like terms: -98.75 + 98.75 = 0.00 0.00 + -20x + x2 = 0 + 98.75 -20x + x2 = 0 + 98.75 Combine like terms: 0 + 98.75 = 98.75 -20x + x2 = 98.75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 98.75 + 100 Reorder the terms: 100 + -20x + x2 = 98.75 + 100 Combine like terms: 98.75 + 100 = 198.75 100 + -20x + x2 = 198.75 Factor a perfect square on the left side: (x + -10)(x + -10) = 198.75 Calculate the square root of the right side: 14.09787218 Break this problem into two subproblems by setting (x + -10) equal to 14.09787218 and -14.09787218.Subproblem 1
x + -10 = 14.09787218 Simplifying x + -10 = 14.09787218 Reorder the terms: -10 + x = 14.09787218 Solving -10 + x = 14.09787218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 14.09787218 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.09787218 + 10 x = 14.09787218 + 10 Combine like terms: 14.09787218 + 10 = 24.09787218 x = 24.09787218 Simplifying x = 24.09787218Subproblem 2
x + -10 = -14.09787218 Simplifying x + -10 = -14.09787218 Reorder the terms: -10 + x = -14.09787218 Solving -10 + x = -14.09787218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -14.09787218 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.09787218 + 10 x = -14.09787218 + 10 Combine like terms: -14.09787218 + 10 = -4.09787218 x = -4.09787218 Simplifying x = -4.09787218Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.09787218, -4.09787218}
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