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Simplifying 28x2 + -5x + -13 = 0 Reorder the terms: -13 + -5x + 28x2 = 0 Solving -13 + -5x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.4642857143 + -0.1785714286x + x2 = 0 Move the constant term to the right: Add '0.4642857143' to each side of the equation. -0.4642857143 + -0.1785714286x + 0.4642857143 + x2 = 0 + 0.4642857143 Reorder the terms: -0.4642857143 + 0.4642857143 + -0.1785714286x + x2 = 0 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + -0.1785714286x + x2 = 0 + 0.4642857143 -0.1785714286x + x2 = 0 + 0.4642857143 Combine like terms: 0 + 0.4642857143 = 0.4642857143 -0.1785714286x + x2 = 0.4642857143 The x term is -0.1785714286x. Take half its coefficient (-0.0892857143). Square it (0.007971938778) and add it to both sides. Add '0.007971938778' to each side of the equation. -0.1785714286x + 0.007971938778 + x2 = 0.4642857143 + 0.007971938778 Reorder the terms: 0.007971938778 + -0.1785714286x + x2 = 0.4642857143 + 0.007971938778 Combine like terms: 0.4642857143 + 0.007971938778 = 0.472257653078 0.007971938778 + -0.1785714286x + x2 = 0.472257653078 Factor a perfect square on the left side: (x + -0.0892857143)(x + -0.0892857143) = 0.472257653078 Calculate the square root of the right side: 0.68721005 Break this problem into two subproblems by setting (x + -0.0892857143) equal to 0.68721005 and -0.68721005.Subproblem 1
x + -0.0892857143 = 0.68721005 Simplifying x + -0.0892857143 = 0.68721005 Reorder the terms: -0.0892857143 + x = 0.68721005 Solving -0.0892857143 + x = 0.68721005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0892857143' to each side of the equation. -0.0892857143 + 0.0892857143 + x = 0.68721005 + 0.0892857143 Combine like terms: -0.0892857143 + 0.0892857143 = 0.0000000000 0.0000000000 + x = 0.68721005 + 0.0892857143 x = 0.68721005 + 0.0892857143 Combine like terms: 0.68721005 + 0.0892857143 = 0.7764957643 x = 0.7764957643 Simplifying x = 0.7764957643Subproblem 2
x + -0.0892857143 = -0.68721005 Simplifying x + -0.0892857143 = -0.68721005 Reorder the terms: -0.0892857143 + x = -0.68721005 Solving -0.0892857143 + x = -0.68721005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0892857143' to each side of the equation. -0.0892857143 + 0.0892857143 + x = -0.68721005 + 0.0892857143 Combine like terms: -0.0892857143 + 0.0892857143 = 0.0000000000 0.0000000000 + x = -0.68721005 + 0.0892857143 x = -0.68721005 + 0.0892857143 Combine like terms: -0.68721005 + 0.0892857143 = -0.5979243357 x = -0.5979243357 Simplifying x = -0.5979243357Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7764957643, -0.5979243357}
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