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Simplifying 0.3x(x + 40) + 0.1x = 16 Reorder the terms: 0.3x(40 + x) + 0.1x = 16 (40 * 0.3x + x * 0.3x) + 0.1x = 16 (12x + 0.3x2) + 0.1x = 16 Reorder the terms: 12x + 0.1x + 0.3x2 = 16 Combine like terms: 12x + 0.1x = 12.1x 12.1x + 0.3x2 = 16 Solving 12.1x + 0.3x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 12.1x + 0.3x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 12.1x + 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'. -53.33333333 + 40.33333333x + x2 = 0 Move the constant term to the right: Add '53.33333333' to each side of the equation. -53.33333333 + 40.33333333x + 53.33333333 + x2 = 0 + 53.33333333 Reorder the terms: -53.33333333 + 53.33333333 + 40.33333333x + x2 = 0 + 53.33333333 Combine like terms: -53.33333333 + 53.33333333 = 0.00000000 0.00000000 + 40.33333333x + x2 = 0 + 53.33333333 40.33333333x + x2 = 0 + 53.33333333 Combine like terms: 0 + 53.33333333 = 53.33333333 40.33333333x + x2 = 53.33333333 The x term is 40.33333333x. Take half its coefficient (20.16666667). Square it (406.6944446) and add it to both sides. Add '406.6944446' to each side of the equation. 40.33333333x + 406.6944446 + x2 = 53.33333333 + 406.6944446 Reorder the terms: 406.6944446 + 40.33333333x + x2 = 53.33333333 + 406.6944446 Combine like terms: 53.33333333 + 406.6944446 = 460.02777793 406.6944446 + 40.33333333x + x2 = 460.02777793 Factor a perfect square on the left side: (x + 20.16666667)(x + 20.16666667) = 460.02777793 Calculate the square root of the right side: 21.448258156 Break this problem into two subproblems by setting (x + 20.16666667) equal to 21.448258156 and -21.448258156.Subproblem 1
x + 20.16666667 = 21.448258156 Simplifying x + 20.16666667 = 21.448258156 Reorder the terms: 20.16666667 + x = 21.448258156 Solving 20.16666667 + x = 21.448258156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.16666667' to each side of the equation. 20.16666667 + -20.16666667 + x = 21.448258156 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + x = 21.448258156 + -20.16666667 x = 21.448258156 + -20.16666667 Combine like terms: 21.448258156 + -20.16666667 = 1.281591486 x = 1.281591486 Simplifying x = 1.281591486Subproblem 2
x + 20.16666667 = -21.448258156 Simplifying x + 20.16666667 = -21.448258156 Reorder the terms: 20.16666667 + x = -21.448258156 Solving 20.16666667 + x = -21.448258156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.16666667' to each side of the equation. 20.16666667 + -20.16666667 + x = -21.448258156 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + x = -21.448258156 + -20.16666667 x = -21.448258156 + -20.16666667 Combine like terms: -21.448258156 + -20.16666667 = -41.614924826 x = -41.614924826 Simplifying x = -41.614924826Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.281591486, -41.614924826}
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