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Simplifying 3x2 = 24x + -20 Reorder the terms: 3x2 = -20 + 24x Solving 3x2 = -20 + 24x Solving for variable 'x'. Reorder the terms: 20 + -24x + 3x2 = -20 + 24x + 20 + -24x Reorder the terms: 20 + -24x + 3x2 = -20 + 20 + 24x + -24x Combine like terms: -20 + 20 = 0 20 + -24x + 3x2 = 0 + 24x + -24x 20 + -24x + 3x2 = 24x + -24x Combine like terms: 24x + -24x = 0 20 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + -8x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + -8x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + -6.666666667 -8x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 -8x + x2 = -6.666666667 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 = -6.666666667 + 16 Reorder the terms: 16 + -8x + x2 = -6.666666667 + 16 Combine like terms: -6.666666667 + 16 = 9.333333333 16 + -8x + x2 = 9.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 9.333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (x + -4) equal to 3.055050463 and -3.055050463.Subproblem 1
x + -4 = 3.055050463 Simplifying x + -4 = 3.055050463 Reorder the terms: -4 + x = 3.055050463 Solving -4 + x = 3.055050463 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 = 3.055050463 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.055050463 + 4 x = 3.055050463 + 4 Combine like terms: 3.055050463 + 4 = 7.055050463 x = 7.055050463 Simplifying x = 7.055050463Subproblem 2
x + -4 = -3.055050463 Simplifying x + -4 = -3.055050463 Reorder the terms: -4 + x = -3.055050463 Solving -4 + x = -3.055050463 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 = -3.055050463 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.055050463 + 4 x = -3.055050463 + 4 Combine like terms: -3.055050463 + 4 = 0.944949537 x = 0.944949537 Simplifying x = 0.944949537Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.055050463, 0.944949537}
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