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Simplifying 3x + 49 = x2 + -14x + -49 Reorder the terms: 49 + 3x = x2 + -14x + -49 Reorder the terms: 49 + 3x = -49 + -14x + x2 Solving 49 + 3x = -49 + -14x + x2 Solving for variable 'x'. Reorder the terms: 49 + 49 + 3x + 14x + -1x2 = -49 + -14x + x2 + 49 + 14x + -1x2 Combine like terms: 49 + 49 = 98 98 + 3x + 14x + -1x2 = -49 + -14x + x2 + 49 + 14x + -1x2 Combine like terms: 3x + 14x = 17x 98 + 17x + -1x2 = -49 + -14x + x2 + 49 + 14x + -1x2 Reorder the terms: 98 + 17x + -1x2 = -49 + 49 + -14x + 14x + x2 + -1x2 Combine like terms: -49 + 49 = 0 98 + 17x + -1x2 = 0 + -14x + 14x + x2 + -1x2 98 + 17x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 98 + 17x + -1x2 = 0 + x2 + -1x2 98 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 98 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -98 + -17x + x2 = 0 Move the constant term to the right: Add '98' to each side of the equation. -98 + -17x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -17x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -17x + x2 = 0 + 98 -17x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -17x + x2 = 98 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 98 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 98 + 72.25 Combine like terms: 98 + 72.25 = 170.25 72.25 + -17x + x2 = 170.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 170.25 Calculate the square root of the right side: 13.047988351 Break this problem into two subproblems by setting (x + -8.5) equal to 13.047988351 and -13.047988351.Subproblem 1
x + -8.5 = 13.047988351 Simplifying x + -8.5 = 13.047988351 Reorder the terms: -8.5 + x = 13.047988351 Solving -8.5 + x = 13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 13.047988351 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 13.047988351 + 8.5 x = 13.047988351 + 8.5 Combine like terms: 13.047988351 + 8.5 = 21.547988351 x = 21.547988351 Simplifying x = 21.547988351Subproblem 2
x + -8.5 = -13.047988351 Simplifying x + -8.5 = -13.047988351 Reorder the terms: -8.5 + x = -13.047988351 Solving -8.5 + x = -13.047988351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -13.047988351 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -13.047988351 + 8.5 x = -13.047988351 + 8.5 Combine like terms: -13.047988351 + 8.5 = -4.547988351 x = -4.547988351 Simplifying x = -4.547988351Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.547988351, -4.547988351}
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