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Simplifying 28x2 + x + -13 = 0 Reorder the terms: -13 + x + 28x2 = 0 Solving -13 + x + 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 + 0.03571428571x + x2 = 0 Move the constant term to the right: Add '0.4642857143' to each side of the equation. -0.4642857143 + 0.03571428571x + 0.4642857143 + x2 = 0 + 0.4642857143 Reorder the terms: -0.4642857143 + 0.4642857143 + 0.03571428571x + x2 = 0 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + 0.03571428571x + x2 = 0 + 0.4642857143 0.03571428571x + x2 = 0 + 0.4642857143 Combine like terms: 0 + 0.4642857143 = 0.4642857143 0.03571428571x + x2 = 0.4642857143 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.03571428571x + 0.25 + x2 = 0.4642857143 + 0.25 Reorder the terms: 0.25 + 0.03571428571x + x2 = 0.4642857143 + 0.25 Combine like terms: 0.4642857143 + 0.25 = 0.7142857143 0.25 + 0.03571428571x + x2 = 0.7142857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.7142857143 Calculate the square root of the right side: 0.845154255 Break this problem into two subproblems by setting (x + 0.5) equal to 0.845154255 and -0.845154255.Subproblem 1
x + 0.5 = 0.845154255 Simplifying x + 0.5 = 0.845154255 Reorder the terms: 0.5 + x = 0.845154255 Solving 0.5 + x = 0.845154255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.845154255 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.845154255 + -0.5 x = 0.845154255 + -0.5 Combine like terms: 0.845154255 + -0.5 = 0.345154255 x = 0.345154255 Simplifying x = 0.345154255Subproblem 2
x + 0.5 = -0.845154255 Simplifying x + 0.5 = -0.845154255 Reorder the terms: 0.5 + x = -0.845154255 Solving 0.5 + x = -0.845154255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.845154255 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.845154255 + -0.5 x = -0.845154255 + -0.5 Combine like terms: -0.845154255 + -0.5 = -1.345154255 x = -1.345154255 Simplifying x = -1.345154255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.345154255, -1.345154255}
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