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Simplifying 0.28x2 + 0.05x + -0.27 = 0 Reorder the terms: -0.27 + 0.05x + 0.28x2 = 0 Solving -0.27 + 0.05x + 0.28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.28 the coefficient of the squared term: Divide each side by '0.28'. -0.9642857143 + 0.1785714286x + x2 = 0 Move the constant term to the right: Add '0.9642857143' to each side of the equation. -0.9642857143 + 0.1785714286x + 0.9642857143 + x2 = 0 + 0.9642857143 Reorder the terms: -0.9642857143 + 0.9642857143 + 0.1785714286x + x2 = 0 + 0.9642857143 Combine like terms: -0.9642857143 + 0.9642857143 = 0.0000000000 0.0000000000 + 0.1785714286x + x2 = 0 + 0.9642857143 0.1785714286x + x2 = 0 + 0.9642857143 Combine like terms: 0 + 0.9642857143 = 0.9642857143 0.1785714286x + x2 = 0.9642857143 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 = 0.9642857143 + 0.007971938778 Reorder the terms: 0.007971938778 + 0.1785714286x + x2 = 0.9642857143 + 0.007971938778 Combine like terms: 0.9642857143 + 0.007971938778 = 0.972257653078 0.007971938778 + 0.1785714286x + x2 = 0.972257653078 Factor a perfect square on the left side: (x + 0.0892857143)(x + 0.0892857143) = 0.972257653078 Calculate the square root of the right side: 0.986031264 Break this problem into two subproblems by setting (x + 0.0892857143) equal to 0.986031264 and -0.986031264.Subproblem 1
x + 0.0892857143 = 0.986031264 Simplifying x + 0.0892857143 = 0.986031264 Reorder the terms: 0.0892857143 + x = 0.986031264 Solving 0.0892857143 + x = 0.986031264 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 = 0.986031264 + -0.0892857143 Combine like terms: 0.0892857143 + -0.0892857143 = 0.0000000000 0.0000000000 + x = 0.986031264 + -0.0892857143 x = 0.986031264 + -0.0892857143 Combine like terms: 0.986031264 + -0.0892857143 = 0.8967455497 x = 0.8967455497 Simplifying x = 0.8967455497Subproblem 2
x + 0.0892857143 = -0.986031264 Simplifying x + 0.0892857143 = -0.986031264 Reorder the terms: 0.0892857143 + x = -0.986031264 Solving 0.0892857143 + x = -0.986031264 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 = -0.986031264 + -0.0892857143 Combine like terms: 0.0892857143 + -0.0892857143 = 0.0000000000 0.0000000000 + x = -0.986031264 + -0.0892857143 x = -0.986031264 + -0.0892857143 Combine like terms: -0.986031264 + -0.0892857143 = -1.0753169783 x = -1.0753169783 Simplifying x = -1.0753169783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8967455497, -1.0753169783}
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