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Simplifying 0.5x + -0.3x(20 + x) = 0.4(20) 0.5x + (20 * -0.3x + x * -0.3x) = 0.4(20) 0.5x + (-6x + -0.3x2) = 0.4(20) Combine like terms: 0.5x + -6x = -5.5x -5.5x + -0.3x2 = 0.4(20) Multiply 0.4 * 20 -5.5x + -0.3x2 = 8 Solving -5.5x + -0.3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -5.5x + -0.3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -5.5x + -0.3x2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 26.66666667 + 18.33333333x + x2 = 0 Move the constant term to the right: Add '-26.66666667' to each side of the equation. 26.66666667 + 18.33333333x + -26.66666667 + x2 = 0 + -26.66666667 Reorder the terms: 26.66666667 + -26.66666667 + 18.33333333x + x2 = 0 + -26.66666667 Combine like terms: 26.66666667 + -26.66666667 = 0.00000000 0.00000000 + 18.33333333x + x2 = 0 + -26.66666667 18.33333333x + x2 = 0 + -26.66666667 Combine like terms: 0 + -26.66666667 = -26.66666667 18.33333333x + x2 = -26.66666667 The x term is 18.33333333x. Take half its coefficient (9.166666665). Square it (84.02777775) and add it to both sides. Add '84.02777775' to each side of the equation. 18.33333333x + 84.02777775 + x2 = -26.66666667 + 84.02777775 Reorder the terms: 84.02777775 + 18.33333333x + x2 = -26.66666667 + 84.02777775 Combine like terms: -26.66666667 + 84.02777775 = 57.36111108 84.02777775 + 18.33333333x + x2 = 57.36111108 Factor a perfect square on the left side: (x + 9.166666665)(x + 9.166666665) = 57.36111108 Calculate the square root of the right side: 7.573711843 Break this problem into two subproblems by setting (x + 9.166666665) equal to 7.573711843 and -7.573711843.Subproblem 1
x + 9.166666665 = 7.573711843 Simplifying x + 9.166666665 = 7.573711843 Reorder the terms: 9.166666665 + x = 7.573711843 Solving 9.166666665 + x = 7.573711843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + x = 7.573711843 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + x = 7.573711843 + -9.166666665 x = 7.573711843 + -9.166666665 Combine like terms: 7.573711843 + -9.166666665 = -1.592954822 x = -1.592954822 Simplifying x = -1.592954822Subproblem 2
x + 9.166666665 = -7.573711843 Simplifying x + 9.166666665 = -7.573711843 Reorder the terms: 9.166666665 + x = -7.573711843 Solving 9.166666665 + x = -7.573711843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.166666665' to each side of the equation. 9.166666665 + -9.166666665 + x = -7.573711843 + -9.166666665 Combine like terms: 9.166666665 + -9.166666665 = 0.000000000 0.000000000 + x = -7.573711843 + -9.166666665 x = -7.573711843 + -9.166666665 Combine like terms: -7.573711843 + -9.166666665 = -16.740378508 x = -16.740378508 Simplifying x = -16.740378508Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.592954822, -16.740378508}
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