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Simplifying 80x2 + x + -594 = 0 Reorder the terms: -594 + x + 80x2 = 0 Solving -594 + x + 80x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -7.425 + 0.0125x + x2 = 0 Move the constant term to the right: Add '7.425' to each side of the equation. -7.425 + 0.0125x + 7.425 + x2 = 0 + 7.425 Reorder the terms: -7.425 + 7.425 + 0.0125x + x2 = 0 + 7.425 Combine like terms: -7.425 + 7.425 = 0.000 0.000 + 0.0125x + x2 = 0 + 7.425 0.0125x + x2 = 0 + 7.425 Combine like terms: 0 + 7.425 = 7.425 0.0125x + x2 = 7.425 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. 0.0125x + 0.25 + x2 = 7.425 + 0.25 Reorder the terms: 0.25 + 0.0125x + x2 = 7.425 + 0.25 Combine like terms: 7.425 + 0.25 = 7.675 0.25 + 0.0125x + x2 = 7.675 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.675 Calculate the square root of the right side: 2.770379035 Break this problem into two subproblems by setting (x + 0.5) equal to 2.770379035 and -2.770379035.Subproblem 1
x + 0.5 = 2.770379035 Simplifying x + 0.5 = 2.770379035 Reorder the terms: 0.5 + x = 2.770379035 Solving 0.5 + x = 2.770379035 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 = 2.770379035 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.770379035 + -0.5 x = 2.770379035 + -0.5 Combine like terms: 2.770379035 + -0.5 = 2.270379035 x = 2.270379035 Simplifying x = 2.270379035Subproblem 2
x + 0.5 = -2.770379035 Simplifying x + 0.5 = -2.770379035 Reorder the terms: 0.5 + x = -2.770379035 Solving 0.5 + x = -2.770379035 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 = -2.770379035 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.770379035 + -0.5 x = -2.770379035 + -0.5 Combine like terms: -2.770379035 + -0.5 = -3.270379035 x = -3.270379035 Simplifying x = -3.270379035Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.270379035, -3.270379035}
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