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Simplifying 15x2 + -15x + -44.1 = 0 Reorder the terms: -44.1 + -15x + 15x2 = 0 Solving -44.1 + -15x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.94 + -1x + x2 = 0 Move the constant term to the right: Add '2.94' to each side of the equation. -2.94 + -1x + 2.94 + x2 = 0 + 2.94 Reorder the terms: -2.94 + 2.94 + -1x + x2 = 0 + 2.94 Combine like terms: -2.94 + 2.94 = 0.00 0.00 + -1x + x2 = 0 + 2.94 -1x + x2 = 0 + 2.94 Combine like terms: 0 + 2.94 = 2.94 -1x + x2 = 2.94 The x term is -1x. 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. -1x + 0.25 + x2 = 2.94 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.94 + 0.25 Combine like terms: 2.94 + 0.25 = 3.19 0.25 + -1x + x2 = 3.19 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.19 Calculate the square root of the right side: 1.78605711 Break this problem into two subproblems by setting (x + -0.5) equal to 1.78605711 and -1.78605711.Subproblem 1
x + -0.5 = 1.78605711 Simplifying x + -0.5 = 1.78605711 Reorder the terms: -0.5 + x = 1.78605711 Solving -0.5 + x = 1.78605711 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 = 1.78605711 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.78605711 + 0.5 x = 1.78605711 + 0.5 Combine like terms: 1.78605711 + 0.5 = 2.28605711 x = 2.28605711 Simplifying x = 2.28605711Subproblem 2
x + -0.5 = -1.78605711 Simplifying x + -0.5 = -1.78605711 Reorder the terms: -0.5 + x = -1.78605711 Solving -0.5 + x = -1.78605711 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 = -1.78605711 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.78605711 + 0.5 x = -1.78605711 + 0.5 Combine like terms: -1.78605711 + 0.5 = -1.28605711 x = -1.28605711 Simplifying x = -1.28605711Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.28605711, -1.28605711}
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