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Simplifying 0.6x(x + 20) + 0.2x = 28 Reorder the terms: 0.6x(20 + x) + 0.2x = 28 (20 * 0.6x + x * 0.6x) + 0.2x = 28 (12x + 0.6x2) + 0.2x = 28 Reorder the terms: 12x + 0.2x + 0.6x2 = 28 Combine like terms: 12x + 0.2x = 12.2x 12.2x + 0.6x2 = 28 Solving 12.2x + 0.6x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 12.2x + 0.6x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 12.2x + 0.6x2 = 0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -46.66666667 + 20.33333333x + x2 = 0 Move the constant term to the right: Add '46.66666667' to each side of the equation. -46.66666667 + 20.33333333x + 46.66666667 + x2 = 0 + 46.66666667 Reorder the terms: -46.66666667 + 46.66666667 + 20.33333333x + x2 = 0 + 46.66666667 Combine like terms: -46.66666667 + 46.66666667 = 0.00000000 0.00000000 + 20.33333333x + x2 = 0 + 46.66666667 20.33333333x + x2 = 0 + 46.66666667 Combine like terms: 0 + 46.66666667 = 46.66666667 20.33333333x + x2 = 46.66666667 The x term is 20.33333333x. Take half its coefficient (10.16666667). Square it (103.3611112) and add it to both sides. Add '103.3611112' to each side of the equation. 20.33333333x + 103.3611112 + x2 = 46.66666667 + 103.3611112 Reorder the terms: 103.3611112 + 20.33333333x + x2 = 46.66666667 + 103.3611112 Combine like terms: 46.66666667 + 103.3611112 = 150.02777787 103.3611112 + 20.33333333x + x2 = 150.02777787 Factor a perfect square on the left side: (x + 10.16666667)(x + 10.16666667) = 150.02777787 Calculate the square root of the right side: 12.248582688 Break this problem into two subproblems by setting (x + 10.16666667) equal to 12.248582688 and -12.248582688.Subproblem 1
x + 10.16666667 = 12.248582688 Simplifying x + 10.16666667 = 12.248582688 Reorder the terms: 10.16666667 + x = 12.248582688 Solving 10.16666667 + x = 12.248582688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.16666667' to each side of the equation. 10.16666667 + -10.16666667 + x = 12.248582688 + -10.16666667 Combine like terms: 10.16666667 + -10.16666667 = 0.00000000 0.00000000 + x = 12.248582688 + -10.16666667 x = 12.248582688 + -10.16666667 Combine like terms: 12.248582688 + -10.16666667 = 2.081916018 x = 2.081916018 Simplifying x = 2.081916018Subproblem 2
x + 10.16666667 = -12.248582688 Simplifying x + 10.16666667 = -12.248582688 Reorder the terms: 10.16666667 + x = -12.248582688 Solving 10.16666667 + x = -12.248582688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.16666667' to each side of the equation. 10.16666667 + -10.16666667 + x = -12.248582688 + -10.16666667 Combine like terms: 10.16666667 + -10.16666667 = 0.00000000 0.00000000 + x = -12.248582688 + -10.16666667 x = -12.248582688 + -10.16666667 Combine like terms: -12.248582688 + -10.16666667 = -22.415249358 x = -22.415249358 Simplifying x = -22.415249358Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.081916018, -22.415249358}
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