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Simplifying 4x2 + x + -2 = 80 Reorder the terms: -2 + x + 4x2 = 80 Solving -2 + x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: -2 + -80 + x + 4x2 = 80 + -80 Combine like terms: -2 + -80 = -82 -82 + x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -82 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20.5 + 0.25x + x2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + 0.25x + 20.5 + x2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + 0.25x + x2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + 0.25x + x2 = 0 + 20.5 0.25x + x2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 0.25x + x2 = 20.5 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. 0.25x + 0.25 + x2 = 20.5 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 20.5 + 0.25 Combine like terms: 20.5 + 0.25 = 20.75 0.25 + 0.25x + x2 = 20.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 20.75 Calculate the square root of the right side: 4.55521679 Break this problem into two subproblems by setting (x + 0.5) equal to 4.55521679 and -4.55521679.Subproblem 1
x + 0.5 = 4.55521679 Simplifying x + 0.5 = 4.55521679 Reorder the terms: 0.5 + x = 4.55521679 Solving 0.5 + x = 4.55521679 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 = 4.55521679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.55521679 + -0.5 x = 4.55521679 + -0.5 Combine like terms: 4.55521679 + -0.5 = 4.05521679 x = 4.05521679 Simplifying x = 4.05521679Subproblem 2
x + 0.5 = -4.55521679 Simplifying x + 0.5 = -4.55521679 Reorder the terms: 0.5 + x = -4.55521679 Solving 0.5 + x = -4.55521679 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 = -4.55521679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.55521679 + -0.5 x = -4.55521679 + -0.5 Combine like terms: -4.55521679 + -0.5 = -5.05521679 x = -5.05521679 Simplifying x = -5.05521679Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05521679, -5.05521679}
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