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Simplifying 5x + -4x(x + 7) = -33 Reorder the terms: 5x + -4x(7 + x) = -33 5x + (7 * -4x + x * -4x) = -33 5x + (-28x + -4x2) = -33 Combine like terms: 5x + -28x = -23x -23x + -4x2 = -33 Solving -23x + -4x2 = -33 Solving for variable 'x'. Reorder the terms: 33 + -23x + -4x2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + -23x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.25 + 5.75x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + 5.75x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + 5.75x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + 5.75x + x2 = 0 + 8.25 5.75x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 5.75x + x2 = 8.25 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 8.25 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 8.25 + 8.265625 Combine like terms: 8.25 + 8.265625 = 16.515625 8.265625 + 5.75x + x2 = 16.515625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 16.515625 Calculate the square root of the right side: 4.063942052 Break this problem into two subproblems by setting (x + 2.875) equal to 4.063942052 and -4.063942052.Subproblem 1
x + 2.875 = 4.063942052 Simplifying x + 2.875 = 4.063942052 Reorder the terms: 2.875 + x = 4.063942052 Solving 2.875 + x = 4.063942052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 4.063942052 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 4.063942052 + -2.875 x = 4.063942052 + -2.875 Combine like terms: 4.063942052 + -2.875 = 1.188942052 x = 1.188942052 Simplifying x = 1.188942052Subproblem 2
x + 2.875 = -4.063942052 Simplifying x + 2.875 = -4.063942052 Reorder the terms: 2.875 + x = -4.063942052 Solving 2.875 + x = -4.063942052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -4.063942052 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -4.063942052 + -2.875 x = -4.063942052 + -2.875 Combine like terms: -4.063942052 + -2.875 = -6.938942052 x = -6.938942052 Simplifying x = -6.938942052Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.188942052, -6.938942052}
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