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Simplifying 90 + -1x(180 + -1x) = 36 90 + (180 * -1x + -1x * -1x) = 36 90 + (-180x + 1x2) = 36 Solving 90 + -180x + 1x2 = 36 Solving for variable 'x'. Reorder the terms: 90 + -36 + -180x + 1x2 = 36 + -36 Combine like terms: 90 + -36 = 54 54 + -180x + 1x2 = 36 + -36 Combine like terms: 36 + -36 = 0 54 + -180x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -180x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -180x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -180x + x2 = 0 + -54 -180x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -180x + x2 = -54 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -54 + 8100 Reorder the terms: 8100 + -180x + x2 = -54 + 8100 Combine like terms: -54 + 8100 = 8046 8100 + -180x + x2 = 8046 Factor a perfect square on the left side: (x + -90)(x + -90) = 8046 Calculate the square root of the right side: 89.699498326 Break this problem into two subproblems by setting (x + -90) equal to 89.699498326 and -89.699498326.Subproblem 1
x + -90 = 89.699498326 Simplifying x + -90 = 89.699498326 Reorder the terms: -90 + x = 89.699498326 Solving -90 + x = 89.699498326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.699498326 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.699498326 + 90 x = 89.699498326 + 90 Combine like terms: 89.699498326 + 90 = 179.699498326 x = 179.699498326 Simplifying x = 179.699498326Subproblem 2
x + -90 = -89.699498326 Simplifying x + -90 = -89.699498326 Reorder the terms: -90 + x = -89.699498326 Solving -90 + x = -89.699498326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.699498326 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.699498326 + 90 x = -89.699498326 + 90 Combine like terms: -89.699498326 + 90 = 0.300501674 x = 0.300501674 Simplifying x = 0.300501674Solution
The solution to the problem is based on the solutions from the subproblems. x = {179.699498326, 0.300501674}
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