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Simplifying 0 = 3x2 + -24x + -7 Reorder the terms: 0 = -7 + -24x + 3x2 Solving 0 = -7 + -24x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 7 = 7 7 + 24x + -3x2 = -7 + -24x + 3x2 + 7 + 24x + -3x2 Reorder the terms: 7 + 24x + -3x2 = -7 + 7 + -24x + 24x + 3x2 + -3x2 Combine like terms: -7 + 7 = 0 7 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2 7 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2 Combine like terms: -24x + 24x = 0 7 + 24x + -3x2 = 0 + 3x2 + -3x2 7 + 24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 7 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + -8x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -8x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -8x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -8x + x2 = 0 + 2.333333333 -8x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -8x + x2 = 2.333333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 2.333333333 + 16 Reorder the terms: 16 + -8x + x2 = 2.333333333 + 16 Combine like terms: 2.333333333 + 16 = 18.333333333 16 + -8x + x2 = 18.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 18.333333333 Calculate the square root of the right side: 4.281744193 Break this problem into two subproblems by setting (x + -4) equal to 4.281744193 and -4.281744193.Subproblem 1
x + -4 = 4.281744193 Simplifying x + -4 = 4.281744193 Reorder the terms: -4 + x = 4.281744193 Solving -4 + x = 4.281744193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.281744193 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.281744193 + 4 x = 4.281744193 + 4 Combine like terms: 4.281744193 + 4 = 8.281744193 x = 8.281744193 Simplifying x = 8.281744193Subproblem 2
x + -4 = -4.281744193 Simplifying x + -4 = -4.281744193 Reorder the terms: -4 + x = -4.281744193 Solving -4 + x = -4.281744193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.281744193 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.281744193 + 4 x = -4.281744193 + 4 Combine like terms: -4.281744193 + 4 = -0.281744193 x = -0.281744193 Simplifying x = -0.281744193Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.281744193, -0.281744193}
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