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Simplifying 4x2 + 21x + -49 = 8x + 4 Reorder the terms: -49 + 21x + 4x2 = 8x + 4 Reorder the terms: -49 + 21x + 4x2 = 4 + 8x Solving -49 + 21x + 4x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: -49 + -4 + 21x + -8x + 4x2 = 4 + 8x + -4 + -8x Combine like terms: -49 + -4 = -53 -53 + 21x + -8x + 4x2 = 4 + 8x + -4 + -8x Combine like terms: 21x + -8x = 13x -53 + 13x + 4x2 = 4 + 8x + -4 + -8x Reorder the terms: -53 + 13x + 4x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 -53 + 13x + 4x2 = 0 + 8x + -8x -53 + 13x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -53 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.25 + 3.25x + x2 = 0 Move the constant term to the right: Add '13.25' to each side of the equation. -13.25 + 3.25x + 13.25 + x2 = 0 + 13.25 Reorder the terms: -13.25 + 13.25 + 3.25x + x2 = 0 + 13.25 Combine like terms: -13.25 + 13.25 = 0.00 0.00 + 3.25x + x2 = 0 + 13.25 3.25x + x2 = 0 + 13.25 Combine like terms: 0 + 13.25 = 13.25 3.25x + x2 = 13.25 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 13.25 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 13.25 + 2.640625 Combine like terms: 13.25 + 2.640625 = 15.890625 2.640625 + 3.25x + x2 = 15.890625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 15.890625 Calculate the square root of the right side: 3.98630468 Break this problem into two subproblems by setting (x + 1.625) equal to 3.98630468 and -3.98630468.Subproblem 1
x + 1.625 = 3.98630468 Simplifying x + 1.625 = 3.98630468 Reorder the terms: 1.625 + x = 3.98630468 Solving 1.625 + x = 3.98630468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.98630468 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.98630468 + -1.625 x = 3.98630468 + -1.625 Combine like terms: 3.98630468 + -1.625 = 2.36130468 x = 2.36130468 Simplifying x = 2.36130468Subproblem 2
x + 1.625 = -3.98630468 Simplifying x + 1.625 = -3.98630468 Reorder the terms: 1.625 + x = -3.98630468 Solving 1.625 + x = -3.98630468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.98630468 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.98630468 + -1.625 x = -3.98630468 + -1.625 Combine like terms: -3.98630468 + -1.625 = -5.61130468 x = -5.61130468 Simplifying x = -5.61130468Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.36130468, -5.61130468}
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