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Simplifying 8x2 + -36x + -45 = 0 Reorder the terms: -45 + -36x + 8x2 = 0 Solving -45 + -36x + 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'. -5.625 + -4.5x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -4.5x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -4.5x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -4.5x + x2 = 0 + 5.625 -4.5x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -4.5x + x2 = 5.625 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 5.625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 5.625 + 5.0625 Combine like terms: 5.625 + 5.0625 = 10.6875 5.0625 + -4.5x + x2 = 10.6875 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 10.6875 Calculate the square root of the right side: 3.269174208 Break this problem into two subproblems by setting (x + -2.25) equal to 3.269174208 and -3.269174208.Subproblem 1
x + -2.25 = 3.269174208 Simplifying x + -2.25 = 3.269174208 Reorder the terms: -2.25 + x = 3.269174208 Solving -2.25 + x = 3.269174208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.269174208 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.269174208 + 2.25 x = 3.269174208 + 2.25 Combine like terms: 3.269174208 + 2.25 = 5.519174208 x = 5.519174208 Simplifying x = 5.519174208Subproblem 2
x + -2.25 = -3.269174208 Simplifying x + -2.25 = -3.269174208 Reorder the terms: -2.25 + x = -3.269174208 Solving -2.25 + x = -3.269174208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.269174208 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.269174208 + 2.25 x = -3.269174208 + 2.25 Combine like terms: -3.269174208 + 2.25 = -1.019174208 x = -1.019174208 Simplifying x = -1.019174208Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.519174208, -1.019174208}
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