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Simplifying 2x2 + -4x = 29 Reorder the terms: -4x + 2x2 = 29 Solving -4x + 2x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + -4x + 2x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + -2x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -2x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -2x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -2x + x2 = 0 + 14.5 -2x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -2x + x2 = 14.5 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 = 14.5 + 1 Reorder the terms: 1 + -2x + x2 = 14.5 + 1 Combine like terms: 14.5 + 1 = 15.5 1 + -2x + x2 = 15.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 15.5 Calculate the square root of the right side: 3.937003937 Break this problem into two subproblems by setting (x + -1) equal to 3.937003937 and -3.937003937.Subproblem 1
x + -1 = 3.937003937 Simplifying x + -1 = 3.937003937 Reorder the terms: -1 + x = 3.937003937 Solving -1 + x = 3.937003937 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 = 3.937003937 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.937003937 + 1 x = 3.937003937 + 1 Combine like terms: 3.937003937 + 1 = 4.937003937 x = 4.937003937 Simplifying x = 4.937003937Subproblem 2
x + -1 = -3.937003937 Simplifying x + -1 = -3.937003937 Reorder the terms: -1 + x = -3.937003937 Solving -1 + x = -3.937003937 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 = -3.937003937 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.937003937 + 1 x = -3.937003937 + 1 Combine like terms: -3.937003937 + 1 = -2.937003937 x = -2.937003937 Simplifying x = -2.937003937Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.937003937, -2.937003937}
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