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Simplifying 0 = 3x2 + 22x + -24 Reorder the terms: 0 = -24 + 22x + 3x2 Solving 0 = -24 + 22x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -22x + -3x2 = -24 + 22x + 3x2 + 24 + -22x + -3x2 Reorder the terms: 24 + -22x + -3x2 = -24 + 24 + 22x + -22x + 3x2 + -3x2 Combine like terms: -24 + 24 = 0 24 + -22x + -3x2 = 0 + 22x + -22x + 3x2 + -3x2 24 + -22x + -3x2 = 22x + -22x + 3x2 + -3x2 Combine like terms: 22x + -22x = 0 24 + -22x + -3x2 = 0 + 3x2 + -3x2 24 + -22x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 24 + -22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -8 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 7.333333333x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 7.333333333x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 7.333333333x + x2 = 0 + 8 7.333333333x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 7.333333333x + x2 = 8 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 8 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 8 + 13.44444445 Combine like terms: 8 + 13.44444445 = 21.44444445 13.44444445 + 7.333333333x + x2 = 21.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 21.44444445 Calculate the square root of the right side: 4.630814664 Break this problem into two subproblems by setting (x + 3.666666667) equal to 4.630814664 and -4.630814664.Subproblem 1
x + 3.666666667 = 4.630814664 Simplifying x + 3.666666667 = 4.630814664 Reorder the terms: 3.666666667 + x = 4.630814664 Solving 3.666666667 + x = 4.630814664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 4.630814664 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 4.630814664 + -3.666666667 x = 4.630814664 + -3.666666667 Combine like terms: 4.630814664 + -3.666666667 = 0.964147997 x = 0.964147997 Simplifying x = 0.964147997Subproblem 2
x + 3.666666667 = -4.630814664 Simplifying x + 3.666666667 = -4.630814664 Reorder the terms: 3.666666667 + x = -4.630814664 Solving 3.666666667 + x = -4.630814664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -4.630814664 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -4.630814664 + -3.666666667 x = -4.630814664 + -3.666666667 Combine like terms: -4.630814664 + -3.666666667 = -8.297481331 x = -8.297481331 Simplifying x = -8.297481331Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.964147997, -8.297481331}
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