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Simplifying 0 = 3x2 + 12x + -20 Reorder the terms: 0 = -20 + 12x + 3x2 Solving 0 = -20 + 12x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + -12x + -3x2 = -20 + 12x + 3x2 + 20 + -12x + -3x2 Reorder the terms: 20 + -12x + -3x2 = -20 + 20 + 12x + -12x + 3x2 + -3x2 Combine like terms: -20 + 20 = 0 20 + -12x + -3x2 = 0 + 12x + -12x + 3x2 + -3x2 20 + -12x + -3x2 = 12x + -12x + 3x2 + -3x2 Combine like terms: 12x + -12x = 0 20 + -12x + -3x2 = 0 + 3x2 + -3x2 20 + -12x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 20 + -12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 4x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 4x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 6.666666667 4x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 4x + x2 = 6.666666667 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 = 6.666666667 + 4 Reorder the terms: 4 + 4x + x2 = 6.666666667 + 4 Combine like terms: 6.666666667 + 4 = 10.666666667 4 + 4x + x2 = 10.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x + 2) equal to 3.265986324 and -3.265986324.Subproblem 1
x + 2 = 3.265986324 Simplifying x + 2 = 3.265986324 Reorder the terms: 2 + x = 3.265986324 Solving 2 + x = 3.265986324 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 = 3.265986324 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.265986324 + -2 x = 3.265986324 + -2 Combine like terms: 3.265986324 + -2 = 1.265986324 x = 1.265986324 Simplifying x = 1.265986324Subproblem 2
x + 2 = -3.265986324 Simplifying x + 2 = -3.265986324 Reorder the terms: 2 + x = -3.265986324 Solving 2 + x = -3.265986324 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 = -3.265986324 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.265986324 + -2 x = -3.265986324 + -2 Combine like terms: -3.265986324 + -2 = -5.265986324 x = -5.265986324 Simplifying x = -5.265986324Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.265986324, -5.265986324}
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