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Simplifying 25x2 + -90x + -117 = 0 Reorder the terms: -117 + -90x + 25x2 = 0 Solving -117 + -90x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -4.68 + -3.6x + x2 = 0 Move the constant term to the right: Add '4.68' to each side of the equation. -4.68 + -3.6x + 4.68 + x2 = 0 + 4.68 Reorder the terms: -4.68 + 4.68 + -3.6x + x2 = 0 + 4.68 Combine like terms: -4.68 + 4.68 = 0.00 0.00 + -3.6x + x2 = 0 + 4.68 -3.6x + x2 = 0 + 4.68 Combine like terms: 0 + 4.68 = 4.68 -3.6x + x2 = 4.68 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 4.68 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 4.68 + 3.24 Combine like terms: 4.68 + 3.24 = 7.92 3.24 + -3.6x + x2 = 7.92 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 7.92 Calculate the square root of the right side: 2.814249456 Break this problem into two subproblems by setting (x + -1.8) equal to 2.814249456 and -2.814249456.Subproblem 1
x + -1.8 = 2.814249456 Simplifying x + -1.8 = 2.814249456 Reorder the terms: -1.8 + x = 2.814249456 Solving -1.8 + x = 2.814249456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.814249456 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.814249456 + 1.8 x = 2.814249456 + 1.8 Combine like terms: 2.814249456 + 1.8 = 4.614249456 x = 4.614249456 Simplifying x = 4.614249456Subproblem 2
x + -1.8 = -2.814249456 Simplifying x + -1.8 = -2.814249456 Reorder the terms: -1.8 + x = -2.814249456 Solving -1.8 + x = -2.814249456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.814249456 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.814249456 + 1.8 x = -2.814249456 + 1.8 Combine like terms: -2.814249456 + 1.8 = -1.014249456 x = -1.014249456 Simplifying x = -1.014249456Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.614249456, -1.014249456}
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