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Simplifying 12x2 + 30x = 47 Reorder the terms: 30x + 12x2 = 47 Solving 30x + 12x2 = 47 Solving for variable 'x'. Reorder the terms: -47 + 30x + 12x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 30x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.916666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '3.916666667' to each side of the equation. -3.916666667 + 2.5x + 3.916666667 + x2 = 0 + 3.916666667 Reorder the terms: -3.916666667 + 3.916666667 + 2.5x + x2 = 0 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 3.916666667 2.5x + x2 = 0 + 3.916666667 Combine like terms: 0 + 3.916666667 = 3.916666667 2.5x + x2 = 3.916666667 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3.916666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3.916666667 + 1.5625 Combine like terms: 3.916666667 + 1.5625 = 5.479166667 1.5625 + 2.5x + x2 = 5.479166667 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 5.479166667 Calculate the square root of the right side: 2.340761984 Break this problem into two subproblems by setting (x + 1.25) equal to 2.340761984 and -2.340761984.Subproblem 1
x + 1.25 = 2.340761984 Simplifying x + 1.25 = 2.340761984 Reorder the terms: 1.25 + x = 2.340761984 Solving 1.25 + x = 2.340761984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.340761984 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.340761984 + -1.25 x = 2.340761984 + -1.25 Combine like terms: 2.340761984 + -1.25 = 1.090761984 x = 1.090761984 Simplifying x = 1.090761984Subproblem 2
x + 1.25 = -2.340761984 Simplifying x + 1.25 = -2.340761984 Reorder the terms: 1.25 + x = -2.340761984 Solving 1.25 + x = -2.340761984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.340761984 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.340761984 + -1.25 x = -2.340761984 + -1.25 Combine like terms: -2.340761984 + -1.25 = -3.590761984 x = -3.590761984 Simplifying x = -3.590761984Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.090761984, -3.590761984}
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