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Simplifying 5x2 + 33x + -19 = 0 Reorder the terms: -19 + 33x + 5x2 = 0 Solving -19 + 33x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.8 + 6.6x + x2 = 0 Move the constant term to the right: Add '3.8' to each side of the equation. -3.8 + 6.6x + 3.8 + x2 = 0 + 3.8 Reorder the terms: -3.8 + 3.8 + 6.6x + x2 = 0 + 3.8 Combine like terms: -3.8 + 3.8 = 0.0 0.0 + 6.6x + x2 = 0 + 3.8 6.6x + x2 = 0 + 3.8 Combine like terms: 0 + 3.8 = 3.8 6.6x + x2 = 3.8 The x term is 6.6x. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6x + 10.89 + x2 = 3.8 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = 3.8 + 10.89 Combine like terms: 3.8 + 10.89 = 14.69 10.89 + 6.6x + x2 = 14.69 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 14.69 Calculate the square root of the right side: 3.832753579 Break this problem into two subproblems by setting (x + 3.3) equal to 3.832753579 and -3.832753579.Subproblem 1
x + 3.3 = 3.832753579 Simplifying x + 3.3 = 3.832753579 Reorder the terms: 3.3 + x = 3.832753579 Solving 3.3 + x = 3.832753579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = 3.832753579 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 3.832753579 + -3.3 x = 3.832753579 + -3.3 Combine like terms: 3.832753579 + -3.3 = 0.532753579 x = 0.532753579 Simplifying x = 0.532753579Subproblem 2
x + 3.3 = -3.832753579 Simplifying x + 3.3 = -3.832753579 Reorder the terms: 3.3 + x = -3.832753579 Solving 3.3 + x = -3.832753579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = -3.832753579 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -3.832753579 + -3.3 x = -3.832753579 + -3.3 Combine like terms: -3.832753579 + -3.3 = -7.132753579 x = -7.132753579 Simplifying x = -7.132753579Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.532753579, -7.132753579}
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