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Simplifying 4x2 + 44x = 153 Reorder the terms: 44x + 4x2 = 153 Solving 44x + 4x2 = 153 Solving for variable 'x'. Reorder the terms: -153 + 44x + 4x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -153 + 44x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -38.25 + 11x + x2 = 0 Move the constant term to the right: Add '38.25' to each side of the equation. -38.25 + 11x + 38.25 + x2 = 0 + 38.25 Reorder the terms: -38.25 + 38.25 + 11x + x2 = 0 + 38.25 Combine like terms: -38.25 + 38.25 = 0.00 0.00 + 11x + x2 = 0 + 38.25 11x + x2 = 0 + 38.25 Combine like terms: 0 + 38.25 = 38.25 11x + x2 = 38.25 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 38.25 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 38.25 + 30.25 Combine like terms: 38.25 + 30.25 = 68.5 30.25 + 11x + x2 = 68.5 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 68.5 Calculate the square root of the right side: 8.276472679 Break this problem into two subproblems by setting (x + 5.5) equal to 8.276472679 and -8.276472679.Subproblem 1
x + 5.5 = 8.276472679 Simplifying x + 5.5 = 8.276472679 Reorder the terms: 5.5 + x = 8.276472679 Solving 5.5 + x = 8.276472679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.276472679 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.276472679 + -5.5 x = 8.276472679 + -5.5 Combine like terms: 8.276472679 + -5.5 = 2.776472679 x = 2.776472679 Simplifying x = 2.776472679Subproblem 2
x + 5.5 = -8.276472679 Simplifying x + 5.5 = -8.276472679 Reorder the terms: 5.5 + x = -8.276472679 Solving 5.5 + x = -8.276472679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.276472679 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.276472679 + -5.5 x = -8.276472679 + -5.5 Combine like terms: -8.276472679 + -5.5 = -13.776472679 x = -13.776472679 Simplifying x = -13.776472679Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.776472679, -13.776472679}
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