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Simplifying 2x2 + 30x + 6 = -2x2 + 4x + 3 Reorder the terms: 6 + 30x + 2x2 = -2x2 + 4x + 3 Reorder the terms: 6 + 30x + 2x2 = 3 + 4x + -2x2 Solving 6 + 30x + 2x2 = 3 + 4x + -2x2 Solving for variable 'x'. Reorder the terms: 6 + -3 + 30x + -4x + 2x2 + 2x2 = 3 + 4x + -2x2 + -3 + -4x + 2x2 Combine like terms: 6 + -3 = 3 3 + 30x + -4x + 2x2 + 2x2 = 3 + 4x + -2x2 + -3 + -4x + 2x2 Combine like terms: 30x + -4x = 26x 3 + 26x + 2x2 + 2x2 = 3 + 4x + -2x2 + -3 + -4x + 2x2 Combine like terms: 2x2 + 2x2 = 4x2 3 + 26x + 4x2 = 3 + 4x + -2x2 + -3 + -4x + 2x2 Reorder the terms: 3 + 26x + 4x2 = 3 + -3 + 4x + -4x + -2x2 + 2x2 Combine like terms: 3 + -3 = 0 3 + 26x + 4x2 = 0 + 4x + -4x + -2x2 + 2x2 3 + 26x + 4x2 = 4x + -4x + -2x2 + 2x2 Combine like terms: 4x + -4x = 0 3 + 26x + 4x2 = 0 + -2x2 + 2x2 3 + 26x + 4x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 3 + 26x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 6.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 6.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 6.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 6.5x + x2 = 0 + -0.75 6.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 6.5x + x2 = -0.75 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -0.75 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -0.75 + 10.5625 Combine like terms: -0.75 + 10.5625 = 9.8125 10.5625 + 6.5x + x2 = 9.8125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (x + 3.25) equal to 3.132491022 and -3.132491022.Subproblem 1
x + 3.25 = 3.132491022 Simplifying x + 3.25 = 3.132491022 Reorder the terms: 3.25 + x = 3.132491022 Solving 3.25 + x = 3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.132491022 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.132491022 + -3.25 x = 3.132491022 + -3.25 Combine like terms: 3.132491022 + -3.25 = -0.117508978 x = -0.117508978 Simplifying x = -0.117508978Subproblem 2
x + 3.25 = -3.132491022 Simplifying x + 3.25 = -3.132491022 Reorder the terms: 3.25 + x = -3.132491022 Solving 3.25 + x = -3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.132491022 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.132491022 + -3.25 x = -3.132491022 + -3.25 Combine like terms: -3.132491022 + -3.25 = -6.382491022 x = -6.382491022 Simplifying x = -6.382491022Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.117508978, -6.382491022}
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