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Simplifying 2x2 + -1x + -90 = 0 Reorder the terms: -90 + -1x + 2x2 = 0 Solving -90 + -1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + -0.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -0.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -0.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -0.5x + x2 = 0 + 45 -0.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -0.5x + x2 = 45 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 45 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 45 + 0.0625 Combine like terms: 45 + 0.0625 = 45.0625 0.0625 + -0.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + -0.25) equal to 6.712860791 and -6.712860791.Subproblem 1
x + -0.25 = 6.712860791 Simplifying x + -0.25 = 6.712860791 Reorder the terms: -0.25 + x = 6.712860791 Solving -0.25 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 6.712860791 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.712860791 + 0.25 x = 6.712860791 + 0.25 Combine like terms: 6.712860791 + 0.25 = 6.962860791 x = 6.962860791 Simplifying x = 6.962860791Subproblem 2
x + -0.25 = -6.712860791 Simplifying x + -0.25 = -6.712860791 Reorder the terms: -0.25 + x = -6.712860791 Solving -0.25 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -6.712860791 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.712860791 + 0.25 x = -6.712860791 + 0.25 Combine like terms: -6.712860791 + 0.25 = -6.462860791 x = -6.462860791 Simplifying x = -6.462860791Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.962860791, -6.462860791}
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