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Simplifying -1x2 + 7.96x + 1 = 0 Reorder the terms: 1 + 7.96x + -1x2 = 0 Solving 1 + 7.96x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -7.96x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -7.96x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -7.96x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7.96x + x2 = 0 + 1 -7.96x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -7.96x + x2 = 1 The x term is -7.96x. Take half its coefficient (-3.98). Square it (15.8404) and add it to both sides. Add '15.8404' to each side of the equation. -7.96x + 15.8404 + x2 = 1 + 15.8404 Reorder the terms: 15.8404 + -7.96x + x2 = 1 + 15.8404 Combine like terms: 1 + 15.8404 = 16.8404 15.8404 + -7.96x + x2 = 16.8404 Factor a perfect square on the left side: (x + -3.98)(x + -3.98) = 16.8404 Calculate the square root of the right side: 4.103705642 Break this problem into two subproblems by setting (x + -3.98) equal to 4.103705642 and -4.103705642.Subproblem 1
x + -3.98 = 4.103705642 Simplifying x + -3.98 = 4.103705642 Reorder the terms: -3.98 + x = 4.103705642 Solving -3.98 + x = 4.103705642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.98' to each side of the equation. -3.98 + 3.98 + x = 4.103705642 + 3.98 Combine like terms: -3.98 + 3.98 = 0.00 0.00 + x = 4.103705642 + 3.98 x = 4.103705642 + 3.98 Combine like terms: 4.103705642 + 3.98 = 8.083705642 x = 8.083705642 Simplifying x = 8.083705642Subproblem 2
x + -3.98 = -4.103705642 Simplifying x + -3.98 = -4.103705642 Reorder the terms: -3.98 + x = -4.103705642 Solving -3.98 + x = -4.103705642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.98' to each side of the equation. -3.98 + 3.98 + x = -4.103705642 + 3.98 Combine like terms: -3.98 + 3.98 = 0.00 0.00 + x = -4.103705642 + 3.98 x = -4.103705642 + 3.98 Combine like terms: -4.103705642 + 3.98 = -0.123705642 x = -0.123705642 Simplifying x = -0.123705642Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.083705642, -0.123705642}
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