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Simplifying 3(x2) + 30x = 130 Reorder the terms: 30x + 3x2 = 130 Solving 30x + 3x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + 30x + 3x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -43.33333333 + 10x + x2 = 0 Move the constant term to the right: Add '43.33333333' to each side of the equation. -43.33333333 + 10x + 43.33333333 + x2 = 0 + 43.33333333 Reorder the terms: -43.33333333 + 43.33333333 + 10x + x2 = 0 + 43.33333333 Combine like terms: -43.33333333 + 43.33333333 = 0.00000000 0.00000000 + 10x + x2 = 0 + 43.33333333 10x + x2 = 0 + 43.33333333 Combine like terms: 0 + 43.33333333 = 43.33333333 10x + x2 = 43.33333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 43.33333333 + 25 Reorder the terms: 25 + 10x + x2 = 43.33333333 + 25 Combine like terms: 43.33333333 + 25 = 68.33333333 25 + 10x + x2 = 68.33333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 68.33333333 Calculate the square root of the right side: 8.266397845 Break this problem into two subproblems by setting (x + 5) equal to 8.266397845 and -8.266397845.Subproblem 1
x + 5 = 8.266397845 Simplifying x + 5 = 8.266397845 Reorder the terms: 5 + x = 8.266397845 Solving 5 + x = 8.266397845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.266397845 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.266397845 + -5 x = 8.266397845 + -5 Combine like terms: 8.266397845 + -5 = 3.266397845 x = 3.266397845 Simplifying x = 3.266397845Subproblem 2
x + 5 = -8.266397845 Simplifying x + 5 = -8.266397845 Reorder the terms: 5 + x = -8.266397845 Solving 5 + x = -8.266397845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.266397845 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.266397845 + -5 x = -8.266397845 + -5 Combine like terms: -8.266397845 + -5 = -13.266397845 x = -13.266397845 Simplifying x = -13.266397845Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.266397845, -13.266397845}
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