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Simplifying 28x2 + -3x + -13 = 0 Reorder the terms: -13 + -3x + 28x2 = 0 Solving -13 + -3x + 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 + -0.1071428571x + x2 = 0 Move the constant term to the right: Add '0.4642857143' to each side of the equation. -0.4642857143 + -0.1071428571x + 0.4642857143 + x2 = 0 + 0.4642857143 Reorder the terms: -0.4642857143 + 0.4642857143 + -0.1071428571x + x2 = 0 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + -0.1071428571x + x2 = 0 + 0.4642857143 -0.1071428571x + x2 = 0 + 0.4642857143 Combine like terms: 0 + 0.4642857143 = 0.4642857143 -0.1071428571x + x2 = 0.4642857143 The x term is -0.1071428571x. Take half its coefficient (-0.05357142855). Square it (0.002869897957) and add it to both sides. Add '0.002869897957' to each side of the equation. -0.1071428571x + 0.002869897957 + x2 = 0.4642857143 + 0.002869897957 Reorder the terms: 0.002869897957 + -0.1071428571x + x2 = 0.4642857143 + 0.002869897957 Combine like terms: 0.4642857143 + 0.002869897957 = 0.467155612257 0.002869897957 + -0.1071428571x + x2 = 0.467155612257 Factor a perfect square on the left side: (x + -0.05357142855)(x + -0.05357142855) = 0.467155612257 Calculate the square root of the right side: 0.683487829 Break this problem into two subproblems by setting (x + -0.05357142855) equal to 0.683487829 and -0.683487829.Subproblem 1
x + -0.05357142855 = 0.683487829 Simplifying x + -0.05357142855 = 0.683487829 Reorder the terms: -0.05357142855 + x = 0.683487829 Solving -0.05357142855 + x = 0.683487829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + x = 0.683487829 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + x = 0.683487829 + 0.05357142855 x = 0.683487829 + 0.05357142855 Combine like terms: 0.683487829 + 0.05357142855 = 0.73705925755 x = 0.73705925755 Simplifying x = 0.73705925755Subproblem 2
x + -0.05357142855 = -0.683487829 Simplifying x + -0.05357142855 = -0.683487829 Reorder the terms: -0.05357142855 + x = -0.683487829 Solving -0.05357142855 + x = -0.683487829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05357142855' to each side of the equation. -0.05357142855 + 0.05357142855 + x = -0.683487829 + 0.05357142855 Combine like terms: -0.05357142855 + 0.05357142855 = 0.00000000000 0.00000000000 + x = -0.683487829 + 0.05357142855 x = -0.683487829 + 0.05357142855 Combine like terms: -0.683487829 + 0.05357142855 = -0.62991640045 x = -0.62991640045 Simplifying x = -0.62991640045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73705925755, -0.62991640045}
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