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Simplifying 0 = 4x2 + -8x + -11 Reorder the terms: 0 = -11 + -8x + 4x2 Solving 0 = -11 + -8x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + 8x + -4x2 = -11 + -8x + 4x2 + 11 + 8x + -4x2 Reorder the terms: 11 + 8x + -4x2 = -11 + 11 + -8x + 8x + 4x2 + -4x2 Combine like terms: -11 + 11 = 0 11 + 8x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2 11 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 11 + 8x + -4x2 = 0 + 4x2 + -4x2 11 + 8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 11 + 8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + -2x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -2x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -2x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -2x + x2 = 0 + 2.75 -2x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -2x + x2 = 2.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 2.75 + 1 Reorder the terms: 1 + -2x + x2 = 2.75 + 1 Combine like terms: 2.75 + 1 = 3.75 1 + -2x + x2 = 3.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -1) equal to 1.936491673 and -1.936491673.Subproblem 1
x + -1 = 1.936491673 Simplifying x + -1 = 1.936491673 Reorder the terms: -1 + x = 1.936491673 Solving -1 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.936491673 + 1 x = 1.936491673 + 1 Combine like terms: 1.936491673 + 1 = 2.936491673 x = 2.936491673 Simplifying x = 2.936491673Subproblem 2
x + -1 = -1.936491673 Simplifying x + -1 = -1.936491673 Reorder the terms: -1 + x = -1.936491673 Solving -1 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.936491673 + 1 x = -1.936491673 + 1 Combine like terms: -1.936491673 + 1 = -0.936491673 x = -0.936491673 Simplifying x = -0.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.936491673, -0.936491673}
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