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Simplifying 8x2 + 90x + -225 = 0 Reorder the terms: -225 + 90x + 8x2 = 0 Solving -225 + 90x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -28.125 + 11.25x + x2 = 0 Move the constant term to the right: Add '28.125' to each side of the equation. -28.125 + 11.25x + 28.125 + x2 = 0 + 28.125 Reorder the terms: -28.125 + 28.125 + 11.25x + x2 = 0 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + 11.25x + x2 = 0 + 28.125 11.25x + x2 = 0 + 28.125 Combine like terms: 0 + 28.125 = 28.125 11.25x + x2 = 28.125 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = 28.125 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = 28.125 + 31.640625 Combine like terms: 28.125 + 31.640625 = 59.765625 31.640625 + 11.25x + x2 = 59.765625 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = 59.765625 Calculate the square root of the right side: 7.730823048 Break this problem into two subproblems by setting (x + 5.625) equal to 7.730823048 and -7.730823048.Subproblem 1
x + 5.625 = 7.730823048 Simplifying x + 5.625 = 7.730823048 Reorder the terms: 5.625 + x = 7.730823048 Solving 5.625 + x = 7.730823048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = 7.730823048 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = 7.730823048 + -5.625 x = 7.730823048 + -5.625 Combine like terms: 7.730823048 + -5.625 = 2.105823048 x = 2.105823048 Simplifying x = 2.105823048Subproblem 2
x + 5.625 = -7.730823048 Simplifying x + 5.625 = -7.730823048 Reorder the terms: 5.625 + x = -7.730823048 Solving 5.625 + x = -7.730823048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = -7.730823048 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = -7.730823048 + -5.625 x = -7.730823048 + -5.625 Combine like terms: -7.730823048 + -5.625 = -13.355823048 x = -13.355823048 Simplifying x = -13.355823048Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.105823048, -13.355823048}
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