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Simplifying 50 = 3.14x2 + 3.14x * 8 Reorder the terms for easier multiplication: 50 = 3.14x2 + 3.14 * 8x Multiply 3.14 * 8 50 = 3.14x2 + 25.12x Reorder the terms: 50 = 25.12x + 3.14x2 Solving 50 = 25.12x + 3.14x2 Solving for variable 'x'. Reorder the terms: 50 + -25.12x + -3.14x2 = 25.12x + -25.12x + 3.14x2 + -3.14x2 Combine like terms: 25.12x + -25.12x = 0.00 50 + -25.12x + -3.14x2 = 0.00 + 3.14x2 + -3.14x2 50 + -25.12x + -3.14x2 = 3.14x2 + -3.14x2 Combine like terms: 3.14x2 + -3.14x2 = 0.00 50 + -25.12x + -3.14x2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -15.92356688 + 8x + x2 = 0 Move the constant term to the right: Add '15.92356688' to each side of the equation. -15.92356688 + 8x + 15.92356688 + x2 = 0 + 15.92356688 Reorder the terms: -15.92356688 + 15.92356688 + 8x + x2 = 0 + 15.92356688 Combine like terms: -15.92356688 + 15.92356688 = 0.00000000 0.00000000 + 8x + x2 = 0 + 15.92356688 8x + x2 = 0 + 15.92356688 Combine like terms: 0 + 15.92356688 = 15.92356688 8x + x2 = 15.92356688 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 15.92356688 + 16 Reorder the terms: 16 + 8x + x2 = 15.92356688 + 16 Combine like terms: 15.92356688 + 16 = 31.92356688 16 + 8x + x2 = 31.92356688 Factor a perfect square on the left side: (x + 4)(x + 4) = 31.92356688 Calculate the square root of the right side: 5.650094413 Break this problem into two subproblems by setting (x + 4) equal to 5.650094413 and -5.650094413.Subproblem 1
x + 4 = 5.650094413 Simplifying x + 4 = 5.650094413 Reorder the terms: 4 + x = 5.650094413 Solving 4 + x = 5.650094413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.650094413 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.650094413 + -4 x = 5.650094413 + -4 Combine like terms: 5.650094413 + -4 = 1.650094413 x = 1.650094413 Simplifying x = 1.650094413Subproblem 2
x + 4 = -5.650094413 Simplifying x + 4 = -5.650094413 Reorder the terms: 4 + x = -5.650094413 Solving 4 + x = -5.650094413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.650094413 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.650094413 + -4 x = -5.650094413 + -4 Combine like terms: -5.650094413 + -4 = -9.650094413 x = -9.650094413 Simplifying x = -9.650094413Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.650094413, -9.650094413}
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