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Simplifying 2x2 + 14x + 8 = 33x + 162 Reorder the terms: 8 + 14x + 2x2 = 33x + 162 Reorder the terms: 8 + 14x + 2x2 = 162 + 33x Solving 8 + 14x + 2x2 = 162 + 33x Solving for variable 'x'. Reorder the terms: 8 + -162 + 14x + -33x + 2x2 = 162 + 33x + -162 + -33x Combine like terms: 8 + -162 = -154 -154 + 14x + -33x + 2x2 = 162 + 33x + -162 + -33x Combine like terms: 14x + -33x = -19x -154 + -19x + 2x2 = 162 + 33x + -162 + -33x Reorder the terms: -154 + -19x + 2x2 = 162 + -162 + 33x + -33x Combine like terms: 162 + -162 = 0 -154 + -19x + 2x2 = 0 + 33x + -33x -154 + -19x + 2x2 = 33x + -33x Combine like terms: 33x + -33x = 0 -154 + -19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77 + -9.5x + x2 = 0 Move the constant term to the right: Add '77' to each side of the equation. -77 + -9.5x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + -9.5x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -9.5x + x2 = 0 + 77 -9.5x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 -9.5x + x2 = 77 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 77 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 77 + 22.5625 Combine like terms: 77 + 22.5625 = 99.5625 22.5625 + -9.5x + x2 = 99.5625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 99.5625 Calculate the square root of the right side: 9.978101022 Break this problem into two subproblems by setting (x + -4.75) equal to 9.978101022 and -9.978101022.Subproblem 1
x + -4.75 = 9.978101022 Simplifying x + -4.75 = 9.978101022 Reorder the terms: -4.75 + x = 9.978101022 Solving -4.75 + x = 9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 9.978101022 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 9.978101022 + 4.75 x = 9.978101022 + 4.75 Combine like terms: 9.978101022 + 4.75 = 14.728101022 x = 14.728101022 Simplifying x = 14.728101022Subproblem 2
x + -4.75 = -9.978101022 Simplifying x + -4.75 = -9.978101022 Reorder the terms: -4.75 + x = -9.978101022 Solving -4.75 + x = -9.978101022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -9.978101022 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -9.978101022 + 4.75 x = -9.978101022 + 4.75 Combine like terms: -9.978101022 + 4.75 = -5.228101022 x = -5.228101022 Simplifying x = -5.228101022Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.728101022, -5.228101022}
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