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Simplifying 2x + 19 = x2 + 16x + 16 Reorder the terms: 19 + 2x = x2 + 16x + 16 Reorder the terms: 19 + 2x = 16 + 16x + x2 Solving 19 + 2x = 16 + 16x + x2 Solving for variable 'x'. Reorder the terms: 19 + -16 + 2x + -16x + -1x2 = 16 + 16x + x2 + -16 + -16x + -1x2 Combine like terms: 19 + -16 = 3 3 + 2x + -16x + -1x2 = 16 + 16x + x2 + -16 + -16x + -1x2 Combine like terms: 2x + -16x = -14x 3 + -14x + -1x2 = 16 + 16x + x2 + -16 + -16x + -1x2 Reorder the terms: 3 + -14x + -1x2 = 16 + -16 + 16x + -16x + x2 + -1x2 Combine like terms: 16 + -16 = 0 3 + -14x + -1x2 = 0 + 16x + -16x + x2 + -1x2 3 + -14x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 3 + -14x + -1x2 = 0 + x2 + -1x2 3 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 14x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 14x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 14x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 14x + x2 = 0 + 3 14x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 14x + x2 = 3 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 3 + 49 Reorder the terms: 49 + 14x + x2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + 14x + x2 = 52 Factor a perfect square on the left side: (x + 7)(x + 7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 7) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 7 = 7.211102551 Simplifying x + 7 = 7.211102551 Reorder the terms: 7 + x = 7.211102551 Solving 7 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.211102551 + -7 x = 7.211102551 + -7 Combine like terms: 7.211102551 + -7 = 0.211102551 x = 0.211102551 Simplifying x = 0.211102551Subproblem 2
x + 7 = -7.211102551 Simplifying x + 7 = -7.211102551 Reorder the terms: 7 + x = -7.211102551 Solving 7 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.211102551 + -7 x = -7.211102551 + -7 Combine like terms: -7.211102551 + -7 = -14.211102551 x = -14.211102551 Simplifying x = -14.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.211102551, -14.211102551}
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