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Simplifying 0.25x2 + -14x + 16 = 0 Reorder the terms: 16 + -14x + 0.25x2 = 0 Solving 16 + -14x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 64 + -56x + x2 = 0 Move the constant term to the right: Add '-64' to each side of the equation. 64 + -56x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -56x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -56x + x2 = 0 + -64 -56x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -56x + x2 = -64 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = -64 + 784 Reorder the terms: 784 + -56x + x2 = -64 + 784 Combine like terms: -64 + 784 = 720 784 + -56x + x2 = 720 Factor a perfect square on the left side: (x + -28)(x + -28) = 720 Calculate the square root of the right side: 26.83281573 Break this problem into two subproblems by setting (x + -28) equal to 26.83281573 and -26.83281573.Subproblem 1
x + -28 = 26.83281573 Simplifying x + -28 = 26.83281573 Reorder the terms: -28 + x = 26.83281573 Solving -28 + x = 26.83281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 26.83281573 + 28 Combine like terms: -28 + 28 = 0 0 + x = 26.83281573 + 28 x = 26.83281573 + 28 Combine like terms: 26.83281573 + 28 = 54.83281573 x = 54.83281573 Simplifying x = 54.83281573Subproblem 2
x + -28 = -26.83281573 Simplifying x + -28 = -26.83281573 Reorder the terms: -28 + x = -26.83281573 Solving -28 + x = -26.83281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -26.83281573 + 28 Combine like terms: -28 + 28 = 0 0 + x = -26.83281573 + 28 x = -26.83281573 + 28 Combine like terms: -26.83281573 + 28 = 1.16718427 x = 1.16718427 Simplifying x = 1.16718427Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.83281573, 1.16718427}
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