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Simplifying (3x2) + (10x) = 144 Reorder the terms: (10x) + (3x2) = 144 Solving (10x) + (3x2) = 144 Solving for variable 'x'. Reorder the terms: -144 + (10x) + (3x2) = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + (10x) + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -48 + (3.333333333x) + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + (3.333333333x) + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + (3.333333333x) + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + (3.333333333x) + x2 = 0 + 48 (3.333333333x) + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 (3.333333333x) + x2 = 48 The x term is (3.333333333x). Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. (3.333333333x) + 2.777777779 + x2 = 48 + 2.777777779 Reorder the terms: 2.777777779 + (3.333333333x) + x2 = 48 + 2.777777779 Combine like terms: 48 + 2.777777779 = 50.777777779 2.777777779 + (3.333333333x) + x2 = 50.777777779 Factor a perfect square on the left side: ((x) + 1.666666667)((x) + 1.666666667) = 50.777777779 Calculate the square root of the right side: 7.125852776 Break this problem into two subproblems by setting ((x) + 1.666666667) equal to 7.125852776 and -7.125852776.Subproblem 1
(x) + 1.666666667 = 7.125852776 Simplifying (x) + 1.666666667 = 7.125852776 x + 1.666666667 = 7.125852776 Reorder the terms: 1.666666667 + x = 7.125852776 Solving 1.666666667 + x = 7.125852776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 7.125852776 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 7.125852776 + -1.666666667 x = 7.125852776 + -1.666666667 Combine like terms: 7.125852776 + -1.666666667 = 5.459186109 x = 5.459186109 Simplifying x = 5.459186109Subproblem 2
(x) + 1.666666667 = -7.125852776 Simplifying (x) + 1.666666667 = -7.125852776 x + 1.666666667 = -7.125852776 Reorder the terms: 1.666666667 + x = -7.125852776 Solving 1.666666667 + x = -7.125852776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -7.125852776 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -7.125852776 + -1.666666667 x = -7.125852776 + -1.666666667 Combine like terms: -7.125852776 + -1.666666667 = -8.792519443 x = -8.792519443 Simplifying x = -8.792519443Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.459186109, -8.792519443}
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