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Simplifying 15x2 + 47x + 8 = 20 Reorder the terms: 8 + 47x + 15x2 = 20 Solving 8 + 47x + 15x2 = 20 Solving for variable 'x'. Reorder the terms: 8 + -20 + 47x + 15x2 = 20 + -20 Combine like terms: 8 + -20 = -12 -12 + 47x + 15x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -12 + 47x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8 + 3.133333333x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3.133333333x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3.133333333x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3.133333333x + x2 = 0 + 0.8 3.133333333x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3.133333333x + x2 = 0.8 The x term is 3.133333333x. Take half its coefficient (1.566666667). Square it (2.454444445) and add it to both sides. Add '2.454444445' to each side of the equation. 3.133333333x + 2.454444445 + x2 = 0.8 + 2.454444445 Reorder the terms: 2.454444445 + 3.133333333x + x2 = 0.8 + 2.454444445 Combine like terms: 0.8 + 2.454444445 = 3.254444445 2.454444445 + 3.133333333x + x2 = 3.254444445 Factor a perfect square on the left side: (x + 1.566666667)(x + 1.566666667) = 3.254444445 Calculate the square root of the right side: 1.804007884 Break this problem into two subproblems by setting (x + 1.566666667) equal to 1.804007884 and -1.804007884.Subproblem 1
x + 1.566666667 = 1.804007884 Simplifying x + 1.566666667 = 1.804007884 Reorder the terms: 1.566666667 + x = 1.804007884 Solving 1.566666667 + x = 1.804007884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.566666667' to each side of the equation. 1.566666667 + -1.566666667 + x = 1.804007884 + -1.566666667 Combine like terms: 1.566666667 + -1.566666667 = 0.000000000 0.000000000 + x = 1.804007884 + -1.566666667 x = 1.804007884 + -1.566666667 Combine like terms: 1.804007884 + -1.566666667 = 0.237341217 x = 0.237341217 Simplifying x = 0.237341217Subproblem 2
x + 1.566666667 = -1.804007884 Simplifying x + 1.566666667 = -1.804007884 Reorder the terms: 1.566666667 + x = -1.804007884 Solving 1.566666667 + x = -1.804007884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.566666667' to each side of the equation. 1.566666667 + -1.566666667 + x = -1.804007884 + -1.566666667 Combine like terms: 1.566666667 + -1.566666667 = 0.000000000 0.000000000 + x = -1.804007884 + -1.566666667 x = -1.804007884 + -1.566666667 Combine like terms: -1.804007884 + -1.566666667 = -3.370674551 x = -3.370674551 Simplifying x = -3.370674551Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.237341217, -3.370674551}
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