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Simplifying 74 = 5x2 + 5x + -17 Reorder the terms: 74 = -17 + 5x + 5x2 Solving 74 = -17 + 5x + 5x2 Solving for variable 'x'. Combine like terms: 74 + 17 = 91 91 + -5x + -5x2 = -17 + 5x + 5x2 + 17 + -5x + -5x2 Reorder the terms: 91 + -5x + -5x2 = -17 + 17 + 5x + -5x + 5x2 + -5x2 Combine like terms: -17 + 17 = 0 91 + -5x + -5x2 = 0 + 5x + -5x + 5x2 + -5x2 91 + -5x + -5x2 = 5x + -5x + 5x2 + -5x2 Combine like terms: 5x + -5x = 0 91 + -5x + -5x2 = 0 + 5x2 + -5x2 91 + -5x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 91 + -5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -18.2 + x + x2 = 0 Move the constant term to the right: Add '18.2' to each side of the equation. -18.2 + x + 18.2 + x2 = 0 + 18.2 Reorder the terms: -18.2 + 18.2 + x + x2 = 0 + 18.2 Combine like terms: -18.2 + 18.2 = 0.0 0.0 + x + x2 = 0 + 18.2 x + x2 = 0 + 18.2 Combine like terms: 0 + 18.2 = 18.2 x + x2 = 18.2 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 = 18.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 18.2 + 0.25 Combine like terms: 18.2 + 0.25 = 18.45 1.25 + x2 = 18.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.45 Calculate the square root of the right side: 4.295346319 Break this problem into two subproblems by setting (x + 0.5) equal to 4.295346319 and -4.295346319.Subproblem 1
x + 0.5 = 4.295346319 Simplifying x + 0.5 = 4.295346319 Reorder the terms: 0.5 + x = 4.295346319 Solving 0.5 + x = 4.295346319 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 = 4.295346319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.295346319 + -0.5 x = 4.295346319 + -0.5 Combine like terms: 4.295346319 + -0.5 = 3.795346319 x = 3.795346319 Simplifying x = 3.795346319Subproblem 2
x + 0.5 = -4.295346319 Simplifying x + 0.5 = -4.295346319 Reorder the terms: 0.5 + x = -4.295346319 Solving 0.5 + x = -4.295346319 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 = -4.295346319 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.295346319 + -0.5 x = -4.295346319 + -0.5 Combine like terms: -4.295346319 + -0.5 = -4.795346319 x = -4.795346319 Simplifying x = -4.795346319Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.795346319, -4.795346319}
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