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Simplifying 0 = (5x2) + 5x + -42 Reorder the terms: 0 = -42 + 5x + (5x2) Solving 0 = -42 + 5x + (5x2) Solving for variable 'x'. Combine like terms: 0 + 42 = 42 42 + -5x + (-5x2) = -42 + 5x + (5x2) + 42 + -5x + (-5x2) Reorder the terms: 42 + -5x + (-5x2) = -42 + 42 + 5x + -5x + (5x2) + (-5x2) Combine like terms: -42 + 42 = 0 42 + -5x + (-5x2) = 0 + 5x + -5x + (5x2) + (-5x2) 42 + -5x + (-5x2) = 5x + -5x + (5x2) + (-5x2) Combine like terms: 5x + -5x = 0 42 + -5x + (-5x2) = 0 + (5x2) + (-5x2) 42 + -5x + (-5x2) = (5x2) + (-5x2) Combine like terms: (5x2) + (-5x2) = 0 42 + -5x + (-5x2) = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.4 + x + x2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + x + 8.4 + x2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + x + x2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + x + x2 = 0 + 8.4 x + x2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 x + x2 = 8.4 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. + 0.25 + x2 = 8.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 8.4 + 0.25 Combine like terms: 8.4 + 0.25 = 8.65 1.25 + x2 = 8.65 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 8.65 Calculate the square root of the right side: 2.941088234 Break this problem into two subproblems by setting ((x) + 0.5) equal to 2.941088234 and -2.941088234.Subproblem 1
(x) + 0.5 = 2.941088234 Simplifying (x) + 0.5 = 2.941088234 x + 0.5 = 2.941088234 Reorder the terms: 0.5 + x = 2.941088234 Solving 0.5 + x = 2.941088234 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 = 2.941088234 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.941088234 + -0.5 x = 2.941088234 + -0.5 Combine like terms: 2.941088234 + -0.5 = 2.441088234 x = 2.441088234 Simplifying x = 2.441088234Subproblem 2
(x) + 0.5 = -2.941088234 Simplifying (x) + 0.5 = -2.941088234 x + 0.5 = -2.941088234 Reorder the terms: 0.5 + x = -2.941088234 Solving 0.5 + x = -2.941088234 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 = -2.941088234 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.941088234 + -0.5 x = -2.941088234 + -0.5 Combine like terms: -2.941088234 + -0.5 = -3.441088234 x = -3.441088234 Simplifying x = -3.441088234Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.441088234, -3.441088234}
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