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Simplifying 7x2 + -96 + -28x = 0 Reorder the terms: -96 + -28x + 7x2 = 0 Solving -96 + -28x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -13.71428571 + -4x + x2 = 0 Move the constant term to the right: Add '13.71428571' to each side of the equation. -13.71428571 + -4x + 13.71428571 + x2 = 0 + 13.71428571 Reorder the terms: -13.71428571 + 13.71428571 + -4x + x2 = 0 + 13.71428571 Combine like terms: -13.71428571 + 13.71428571 = 0.00000000 0.00000000 + -4x + x2 = 0 + 13.71428571 -4x + x2 = 0 + 13.71428571 Combine like terms: 0 + 13.71428571 = 13.71428571 -4x + x2 = 13.71428571 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 13.71428571 + 4 Reorder the terms: 4 + -4x + x2 = 13.71428571 + 4 Combine like terms: 13.71428571 + 4 = 17.71428571 4 + -4x + x2 = 17.71428571 Factor a perfect square on the left side: (x + -2)(x + -2) = 17.71428571 Calculate the square root of the right side: 4.208834246 Break this problem into two subproblems by setting (x + -2) equal to 4.208834246 and -4.208834246.Subproblem 1
x + -2 = 4.208834246 Simplifying x + -2 = 4.208834246 Reorder the terms: -2 + x = 4.208834246 Solving -2 + x = 4.208834246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.208834246 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.208834246 + 2 x = 4.208834246 + 2 Combine like terms: 4.208834246 + 2 = 6.208834246 x = 6.208834246 Simplifying x = 6.208834246Subproblem 2
x + -2 = -4.208834246 Simplifying x + -2 = -4.208834246 Reorder the terms: -2 + x = -4.208834246 Solving -2 + x = -4.208834246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.208834246 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.208834246 + 2 x = -4.208834246 + 2 Combine like terms: -4.208834246 + 2 = -2.208834246 x = -2.208834246 Simplifying x = -2.208834246Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.208834246, -2.208834246}
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