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Simplifying 7x2 + -28x + -24 = 0 Reorder the terms: -24 + -28x + 7x2 = 0 Solving -24 + -28x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -4x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -4x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -4x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -4x + x2 = 0 + 3.428571429 -4x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -4x + x2 = 3.428571429 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 3.428571429 + 4 Reorder the terms: 4 + -4x + x2 = 3.428571429 + 4 Combine like terms: 3.428571429 + 4 = 7.428571429 4 + -4x + x2 = 7.428571429 Factor a perfect square on the left side: (x + -2)(x + -2) = 7.428571429 Calculate the square root of the right side: 2.725540576 Break this problem into two subproblems by setting (x + -2) equal to 2.725540576 and -2.725540576.Subproblem 1
x + -2 = 2.725540576 Simplifying x + -2 = 2.725540576 Reorder the terms: -2 + x = 2.725540576 Solving -2 + x = 2.725540576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.725540576 + 2 x = 2.725540576 + 2 Combine like terms: 2.725540576 + 2 = 4.725540576 x = 4.725540576 Simplifying x = 4.725540576Subproblem 2
x + -2 = -2.725540576 Simplifying x + -2 = -2.725540576 Reorder the terms: -2 + x = -2.725540576 Solving -2 + x = -2.725540576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.725540576 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.725540576 + 2 x = -2.725540576 + 2 Combine like terms: -2.725540576 + 2 = -0.725540576 x = -0.725540576 Simplifying x = -0.725540576Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.725540576, -0.725540576}
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