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Simplifying x2 = 45 + 8x Solving x2 = 45 + 8x Solving for variable 'x'. Reorder the terms: -45 + -8x + x2 = 45 + 8x + -45 + -8x Reorder the terms: -45 + -8x + x2 = 45 + -45 + 8x + -8x Combine like terms: 45 + -45 = 0 -45 + -8x + x2 = 0 + 8x + -8x -45 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -45 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -8x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -8x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -8x + x2 = 0 + 45 -8x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -8x + x2 = 45 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 45 + 16 Reorder the terms: 16 + -8x + x2 = 45 + 16 Combine like terms: 45 + 16 = 61 16 + -8x + x2 = 61 Factor a perfect square on the left side: (x + -4)(x + -4) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -4) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -4 = 7.810249676 Simplifying x + -4 = 7.810249676 Reorder the terms: -4 + x = 7.810249676 Solving -4 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.810249676 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.810249676 + 4 x = 7.810249676 + 4 Combine like terms: 7.810249676 + 4 = 11.810249676 x = 11.810249676 Simplifying x = 11.810249676Subproblem 2
x + -4 = -7.810249676 Simplifying x + -4 = -7.810249676 Reorder the terms: -4 + x = -7.810249676 Solving -4 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.810249676 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.810249676 + 4 x = -7.810249676 + 4 Combine like terms: -7.810249676 + 4 = -3.810249676 x = -3.810249676 Simplifying x = -3.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.810249676, -3.810249676}
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