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Simplifying 5x2 + -12x + -100 = 0 Reorder the terms: -100 + -12x + 5x2 = 0 Solving -100 + -12x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -20 + -2.4x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2.4x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2.4x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2.4x + x2 = 0 + 20 -2.4x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2.4x + x2 = 20 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 20 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 20 + 1.44 Combine like terms: 20 + 1.44 = 21.44 1.44 + -2.4x + x2 = 21.44 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 21.44 Calculate the square root of the right side: 4.630334761 Break this problem into two subproblems by setting (x + -1.2) equal to 4.630334761 and -4.630334761.Subproblem 1
x + -1.2 = 4.630334761 Simplifying x + -1.2 = 4.630334761 Reorder the terms: -1.2 + x = 4.630334761 Solving -1.2 + x = 4.630334761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 4.630334761 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 4.630334761 + 1.2 x = 4.630334761 + 1.2 Combine like terms: 4.630334761 + 1.2 = 5.830334761 x = 5.830334761 Simplifying x = 5.830334761Subproblem 2
x + -1.2 = -4.630334761 Simplifying x + -1.2 = -4.630334761 Reorder the terms: -1.2 + x = -4.630334761 Solving -1.2 + x = -4.630334761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -4.630334761 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -4.630334761 + 1.2 x = -4.630334761 + 1.2 Combine like terms: -4.630334761 + 1.2 = -3.430334761 x = -3.430334761 Simplifying x = -3.430334761Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.830334761, -3.430334761}
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