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Simplifying 56 + -31.3x + x2 = 0 Solving 56 + -31.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -31.3x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -31.3x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -31.3x + x2 = 0 + -56 -31.3x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -31.3x + x2 = -56 The x term is -31.3x. Take half its coefficient (-15.65). Square it (244.9225) and add it to both sides. Add '244.9225' to each side of the equation. -31.3x + 244.9225 + x2 = -56 + 244.9225 Reorder the terms: 244.9225 + -31.3x + x2 = -56 + 244.9225 Combine like terms: -56 + 244.9225 = 188.9225 244.9225 + -31.3x + x2 = 188.9225 Factor a perfect square on the left side: (x + -15.65)(x + -15.65) = 188.9225 Calculate the square root of the right side: 13.744908148 Break this problem into two subproblems by setting (x + -15.65) equal to 13.744908148 and -13.744908148.Subproblem 1
x + -15.65 = 13.744908148 Simplifying x + -15.65 = 13.744908148 Reorder the terms: -15.65 + x = 13.744908148 Solving -15.65 + x = 13.744908148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.65' to each side of the equation. -15.65 + 15.65 + x = 13.744908148 + 15.65 Combine like terms: -15.65 + 15.65 = 0.00 0.00 + x = 13.744908148 + 15.65 x = 13.744908148 + 15.65 Combine like terms: 13.744908148 + 15.65 = 29.394908148 x = 29.394908148 Simplifying x = 29.394908148Subproblem 2
x + -15.65 = -13.744908148 Simplifying x + -15.65 = -13.744908148 Reorder the terms: -15.65 + x = -13.744908148 Solving -15.65 + x = -13.744908148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.65' to each side of the equation. -15.65 + 15.65 + x = -13.744908148 + 15.65 Combine like terms: -15.65 + 15.65 = 0.00 0.00 + x = -13.744908148 + 15.65 x = -13.744908148 + 15.65 Combine like terms: -13.744908148 + 15.65 = 1.905091852 x = 1.905091852 Simplifying x = 1.905091852Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.394908148, 1.905091852}
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