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Simplifying (4x2 + -8x + 16) + -49 = 0 Reorder the terms: (16 + -8x + 4x2) + -49 = 0 Remove parenthesis around (16 + -8x + 4x2) 16 + -8x + 4x2 + -49 = 0 Reorder the terms: 16 + -49 + -8x + 4x2 = 0 Combine like terms: 16 + -49 = -33 -33 + -8x + 4x2 = 0 Solving -33 + -8x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + -2x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -2x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -2x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -2x + x2 = 0 + 8.25 -2x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -2x + x2 = 8.25 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 = 8.25 + 1 Reorder the terms: 1 + -2x + x2 = 8.25 + 1 Combine like terms: 8.25 + 1 = 9.25 1 + -2x + x2 = 9.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -1) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -1 = 3.041381265 Simplifying x + -1 = 3.041381265 Reorder the terms: -1 + x = 3.041381265 Solving -1 + x = 3.041381265 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 = 3.041381265 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.041381265 + 1 x = 3.041381265 + 1 Combine like terms: 3.041381265 + 1 = 4.041381265 x = 4.041381265 Simplifying x = 4.041381265Subproblem 2
x + -1 = -3.041381265 Simplifying x + -1 = -3.041381265 Reorder the terms: -1 + x = -3.041381265 Solving -1 + x = -3.041381265 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 = -3.041381265 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.041381265 + 1 x = -3.041381265 + 1 Combine like terms: -3.041381265 + 1 = -2.041381265 x = -2.041381265 Simplifying x = -2.041381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.041381265, -2.041381265}
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