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Simplifying 0.3x(x + 90) + 0.1x = 3 Reorder the terms: 0.3x(90 + x) + 0.1x = 3 (90 * 0.3x + x * 0.3x) + 0.1x = 3 (27x + 0.3x2) + 0.1x = 3 Reorder the terms: 27x + 0.1x + 0.3x2 = 3 Combine like terms: 27x + 0.1x = 27.1x 27.1x + 0.3x2 = 3 Solving 27.1x + 0.3x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 27.1x + 0.3x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 27.1x + 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'. -10 + 90.33333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 90.33333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 90.33333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 90.33333333x + x2 = 0 + 10 90.33333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 90.33333333x + x2 = 10 The x term is 90.33333333x. Take half its coefficient (45.16666667). Square it (2040.027778) and add it to both sides. Add '2040.027778' to each side of the equation. 90.33333333x + 2040.027778 + x2 = 10 + 2040.027778 Reorder the terms: 2040.027778 + 90.33333333x + x2 = 10 + 2040.027778 Combine like terms: 10 + 2040.027778 = 2050.027778 2040.027778 + 90.33333333x + x2 = 2050.027778 Factor a perfect square on the left side: (x + 45.16666667)(x + 45.16666667) = 2050.027778 Calculate the square root of the right side: 45.277232446 Break this problem into two subproblems by setting (x + 45.16666667) equal to 45.277232446 and -45.277232446.Subproblem 1
x + 45.16666667 = 45.277232446 Simplifying x + 45.16666667 = 45.277232446 Reorder the terms: 45.16666667 + x = 45.277232446 Solving 45.16666667 + x = 45.277232446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.16666667' to each side of the equation. 45.16666667 + -45.16666667 + x = 45.277232446 + -45.16666667 Combine like terms: 45.16666667 + -45.16666667 = 0.00000000 0.00000000 + x = 45.277232446 + -45.16666667 x = 45.277232446 + -45.16666667 Combine like terms: 45.277232446 + -45.16666667 = 0.110565776 x = 0.110565776 Simplifying x = 0.110565776Subproblem 2
x + 45.16666667 = -45.277232446 Simplifying x + 45.16666667 = -45.277232446 Reorder the terms: 45.16666667 + x = -45.277232446 Solving 45.16666667 + x = -45.277232446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45.16666667' to each side of the equation. 45.16666667 + -45.16666667 + x = -45.277232446 + -45.16666667 Combine like terms: 45.16666667 + -45.16666667 = 0.00000000 0.00000000 + x = -45.277232446 + -45.16666667 x = -45.277232446 + -45.16666667 Combine like terms: -45.277232446 + -45.16666667 = -90.443899116 x = -90.443899116 Simplifying x = -90.443899116Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110565776, -90.443899116}
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