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Simplifying 3x2 + 2x + -20 = 20x + -7 Reorder the terms: -20 + 2x + 3x2 = 20x + -7 Reorder the terms: -20 + 2x + 3x2 = -7 + 20x Solving -20 + 2x + 3x2 = -7 + 20x Solving for variable 'x'. Reorder the terms: -20 + 7 + 2x + -20x + 3x2 = -7 + 20x + 7 + -20x Combine like terms: -20 + 7 = -13 -13 + 2x + -20x + 3x2 = -7 + 20x + 7 + -20x Combine like terms: 2x + -20x = -18x -13 + -18x + 3x2 = -7 + 20x + 7 + -20x Reorder the terms: -13 + -18x + 3x2 = -7 + 7 + 20x + -20x Combine like terms: -7 + 7 = 0 -13 + -18x + 3x2 = 0 + 20x + -20x -13 + -18x + 3x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -13 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -6x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -6x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + 4.333333333 -6x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -6x + x2 = 4.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 4.333333333 + 9 Reorder the terms: 9 + -6x + x2 = 4.333333333 + 9 Combine like terms: 4.333333333 + 9 = 13.333333333 9 + -6x + x2 = 13.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 13.333333333 Calculate the square root of the right side: 3.651483717 Break this problem into two subproblems by setting (x + -3) equal to 3.651483717 and -3.651483717.Subproblem 1
x + -3 = 3.651483717 Simplifying x + -3 = 3.651483717 Reorder the terms: -3 + x = 3.651483717 Solving -3 + x = 3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.651483717 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.651483717 + 3 x = 3.651483717 + 3 Combine like terms: 3.651483717 + 3 = 6.651483717 x = 6.651483717 Simplifying x = 6.651483717Subproblem 2
x + -3 = -3.651483717 Simplifying x + -3 = -3.651483717 Reorder the terms: -3 + x = -3.651483717 Solving -3 + x = -3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.651483717 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.651483717 + 3 x = -3.651483717 + 3 Combine like terms: -3.651483717 + 3 = -0.651483717 x = -0.651483717 Simplifying x = -0.651483717Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.651483717, -0.651483717}
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