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Simplifying 107 = 5x2 + 2x Reorder the terms: 107 = 2x + 5x2 Solving 107 = 2x + 5x2 Solving for variable 'x'. Reorder the terms: 107 + -2x + -5x2 = 2x + -2x + 5x2 + -5x2 Combine like terms: 2x + -2x = 0 107 + -2x + -5x2 = 0 + 5x2 + -5x2 107 + -2x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 107 + -2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -21.4 + 0.4x + x2 = 0 Move the constant term to the right: Add '21.4' to each side of the equation. -21.4 + 0.4x + 21.4 + x2 = 0 + 21.4 Reorder the terms: -21.4 + 21.4 + 0.4x + x2 = 0 + 21.4 Combine like terms: -21.4 + 21.4 = 0.0 0.0 + 0.4x + x2 = 0 + 21.4 0.4x + x2 = 0 + 21.4 Combine like terms: 0 + 21.4 = 21.4 0.4x + x2 = 21.4 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 21.4 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 21.4 + 0.04 Combine like terms: 21.4 + 0.04 = 21.44 0.04 + 0.4x + x2 = 21.44 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 21.44 Calculate the square root of the right side: 4.630334761 Break this problem into two subproblems by setting (x + 0.2) equal to 4.630334761 and -4.630334761.Subproblem 1
x + 0.2 = 4.630334761 Simplifying x + 0.2 = 4.630334761 Reorder the terms: 0.2 + x = 4.630334761 Solving 0.2 + x = 4.630334761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 4.630334761 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 4.630334761 + -0.2 x = 4.630334761 + -0.2 Combine like terms: 4.630334761 + -0.2 = 4.430334761 x = 4.430334761 Simplifying x = 4.430334761Subproblem 2
x + 0.2 = -4.630334761 Simplifying x + 0.2 = -4.630334761 Reorder the terms: 0.2 + x = -4.630334761 Solving 0.2 + x = -4.630334761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -4.630334761 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -4.630334761 + -0.2 x = -4.630334761 + -0.2 Combine like terms: -4.630334761 + -0.2 = -4.830334761 x = -4.830334761 Simplifying x = -4.830334761Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.430334761, -4.830334761}
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