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Simplifying 5X2 + -22X + -75 = 0 Reorder the terms: -75 + -22X + 5X2 = 0 Solving -75 + -22X + 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'. -15 + -4.4X + X2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -4.4X + 15 + X2 = 0 + 15 Reorder the terms: -15 + 15 + -4.4X + X2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4.4X + X2 = 0 + 15 -4.4X + X2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4.4X + X2 = 15 The X term is -4.4X. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4X + 4.84 + X2 = 15 + 4.84 Reorder the terms: 4.84 + -4.4X + X2 = 15 + 4.84 Combine like terms: 15 + 4.84 = 19.84 4.84 + -4.4X + X2 = 19.84 Factor a perfect square on the left side: (X + -2.2)(X + -2.2) = 19.84 Calculate the square root of the right side: 4.45421149 Break this problem into two subproblems by setting (X + -2.2) equal to 4.45421149 and -4.45421149.Subproblem 1
X + -2.2 = 4.45421149 Simplifying X + -2.2 = 4.45421149 Reorder the terms: -2.2 + X = 4.45421149 Solving -2.2 + X = 4.45421149 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + X = 4.45421149 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + X = 4.45421149 + 2.2 X = 4.45421149 + 2.2 Combine like terms: 4.45421149 + 2.2 = 6.65421149 X = 6.65421149 Simplifying X = 6.65421149Subproblem 2
X + -2.2 = -4.45421149 Simplifying X + -2.2 = -4.45421149 Reorder the terms: -2.2 + X = -4.45421149 Solving -2.2 + X = -4.45421149 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + X = -4.45421149 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + X = -4.45421149 + 2.2 X = -4.45421149 + 2.2 Combine like terms: -4.45421149 + 2.2 = -2.25421149 X = -2.25421149 Simplifying X = -2.25421149Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.65421149, -2.25421149}
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