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Simplifying -3x2 + -24x + 12 = 10 Reorder the terms: 12 + -24x + -3x2 = 10 Solving 12 + -24x + -3x2 = 10 Solving for variable 'x'. Reorder the terms: 12 + -10 + -24x + -3x2 = 10 + -10 Combine like terms: 12 + -10 = 2 2 + -24x + -3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 2 + -24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.6666666667 + 8x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 8x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 8x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 8x + x2 = 0 + 0.6666666667 8x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 8x + x2 = 0.6666666667 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 = 0.6666666667 + 16 Reorder the terms: 16 + 8x + x2 = 0.6666666667 + 16 Combine like terms: 0.6666666667 + 16 = 16.6666666667 16 + 8x + x2 = 16.6666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.6666666667 Calculate the square root of the right side: 4.082482905 Break this problem into two subproblems by setting (x + 4) equal to 4.082482905 and -4.082482905.Subproblem 1
x + 4 = 4.082482905 Simplifying x + 4 = 4.082482905 Reorder the terms: 4 + x = 4.082482905 Solving 4 + x = 4.082482905 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 = 4.082482905 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.082482905 + -4 x = 4.082482905 + -4 Combine like terms: 4.082482905 + -4 = 0.082482905 x = 0.082482905 Simplifying x = 0.082482905Subproblem 2
x + 4 = -4.082482905 Simplifying x + 4 = -4.082482905 Reorder the terms: 4 + x = -4.082482905 Solving 4 + x = -4.082482905 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 = -4.082482905 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.082482905 + -4 x = -4.082482905 + -4 Combine like terms: -4.082482905 + -4 = -8.082482905 x = -8.082482905 Simplifying x = -8.082482905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082482905, -8.082482905}
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