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Simplifying 0 = -12x2 + -55x + 20 Reorder the terms: 0 = 20 + -55x + -12x2 Solving 0 = 20 + -55x + -12x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 55x + 12x2 = 20 + -55x + -12x2 + -20 + 55x + 12x2 Reorder the terms: -20 + 55x + 12x2 = 20 + -20 + -55x + 55x + -12x2 + 12x2 Combine like terms: 20 + -20 = 0 -20 + 55x + 12x2 = 0 + -55x + 55x + -12x2 + 12x2 -20 + 55x + 12x2 = -55x + 55x + -12x2 + 12x2 Combine like terms: -55x + 55x = 0 -20 + 55x + 12x2 = 0 + -12x2 + 12x2 -20 + 55x + 12x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -20 + 55x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.666666667 + 4.583333333x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 4.583333333x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 4.583333333x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 4.583333333x + x2 = 0 + 1.666666667 4.583333333x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 4.583333333x + x2 = 1.666666667 The x term is 4.583333333x. Take half its coefficient (2.291666667). Square it (5.251736113) and add it to both sides. Add '5.251736113' to each side of the equation. 4.583333333x + 5.251736113 + x2 = 1.666666667 + 5.251736113 Reorder the terms: 5.251736113 + 4.583333333x + x2 = 1.666666667 + 5.251736113 Combine like terms: 1.666666667 + 5.251736113 = 6.91840278 5.251736113 + 4.583333333x + x2 = 6.91840278 Factor a perfect square on the left side: (x + 2.291666667)(x + 2.291666667) = 6.91840278 Calculate the square root of the right side: 2.630285684 Break this problem into two subproblems by setting (x + 2.291666667) equal to 2.630285684 and -2.630285684.Subproblem 1
x + 2.291666667 = 2.630285684 Simplifying x + 2.291666667 = 2.630285684 Reorder the terms: 2.291666667 + x = 2.630285684 Solving 2.291666667 + x = 2.630285684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.291666667' to each side of the equation. 2.291666667 + -2.291666667 + x = 2.630285684 + -2.291666667 Combine like terms: 2.291666667 + -2.291666667 = 0.000000000 0.000000000 + x = 2.630285684 + -2.291666667 x = 2.630285684 + -2.291666667 Combine like terms: 2.630285684 + -2.291666667 = 0.338619017 x = 0.338619017 Simplifying x = 0.338619017Subproblem 2
x + 2.291666667 = -2.630285684 Simplifying x + 2.291666667 = -2.630285684 Reorder the terms: 2.291666667 + x = -2.630285684 Solving 2.291666667 + x = -2.630285684 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.291666667' to each side of the equation. 2.291666667 + -2.291666667 + x = -2.630285684 + -2.291666667 Combine like terms: 2.291666667 + -2.291666667 = 0.000000000 0.000000000 + x = -2.630285684 + -2.291666667 x = -2.630285684 + -2.291666667 Combine like terms: -2.630285684 + -2.291666667 = -4.921952351 x = -4.921952351 Simplifying x = -4.921952351Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.338619017, -4.921952351}
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