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Simplifying 5x2 + 3x + -44 = 0 Reorder the terms: -44 + 3x + 5x2 = 0 Solving -44 + 3x + 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'. -8.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + 0.6x + 8.8 + x2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + 0.6x + x2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + 0.6x + x2 = 0 + 8.8 0.6x + x2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 0.6x + x2 = 8.8 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 8.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 8.8 + 0.09 Combine like terms: 8.8 + 0.09 = 8.89 0.09 + 0.6x + x2 = 8.89 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 8.89 Calculate the square root of the right side: 2.981610303 Break this problem into two subproblems by setting (x + 0.3) equal to 2.981610303 and -2.981610303.Subproblem 1
x + 0.3 = 2.981610303 Simplifying x + 0.3 = 2.981610303 Reorder the terms: 0.3 + x = 2.981610303 Solving 0.3 + x = 2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.981610303 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.981610303 + -0.3 x = 2.981610303 + -0.3 Combine like terms: 2.981610303 + -0.3 = 2.681610303 x = 2.681610303 Simplifying x = 2.681610303Subproblem 2
x + 0.3 = -2.981610303 Simplifying x + 0.3 = -2.981610303 Reorder the terms: 0.3 + x = -2.981610303 Solving 0.3 + x = -2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.981610303 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.981610303 + -0.3 x = -2.981610303 + -0.3 Combine like terms: -2.981610303 + -0.3 = -3.281610303 x = -3.281610303 Simplifying x = -3.281610303Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.681610303, -3.281610303}
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