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Simplifying 3x2 + 30x = 77 Reorder the terms: 30x + 3x2 = 77 Solving 30x + 3x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + 30x + 3x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.66666667 + 10x + x2 = 0 Move the constant term to the right: Add '25.66666667' to each side of the equation. -25.66666667 + 10x + 25.66666667 + x2 = 0 + 25.66666667 Reorder the terms: -25.66666667 + 25.66666667 + 10x + x2 = 0 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + 10x + x2 = 0 + 25.66666667 10x + x2 = 0 + 25.66666667 Combine like terms: 0 + 25.66666667 = 25.66666667 10x + x2 = 25.66666667 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 = 25.66666667 + 25 Reorder the terms: 25 + 10x + x2 = 25.66666667 + 25 Combine like terms: 25.66666667 + 25 = 50.66666667 25 + 10x + x2 = 50.66666667 Factor a perfect square on the left side: (x + 5)(x + 5) = 50.66666667 Calculate the square root of the right side: 7.118052168 Break this problem into two subproblems by setting (x + 5) equal to 7.118052168 and -7.118052168.Subproblem 1
x + 5 = 7.118052168 Simplifying x + 5 = 7.118052168 Reorder the terms: 5 + x = 7.118052168 Solving 5 + x = 7.118052168 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 = 7.118052168 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.118052168 + -5 x = 7.118052168 + -5 Combine like terms: 7.118052168 + -5 = 2.118052168 x = 2.118052168 Simplifying x = 2.118052168Subproblem 2
x + 5 = -7.118052168 Simplifying x + 5 = -7.118052168 Reorder the terms: 5 + x = -7.118052168 Solving 5 + x = -7.118052168 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 = -7.118052168 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.118052168 + -5 x = -7.118052168 + -5 Combine like terms: -7.118052168 + -5 = -12.118052168 x = -12.118052168 Simplifying x = -12.118052168Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.118052168, -12.118052168}
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