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Simplifying 9x(x + -8) + 5 = 0 Reorder the terms: 9x(-8 + x) + 5 = 0 (-8 * 9x + x * 9x) + 5 = 0 (-72x + 9x2) + 5 = 0 Reorder the terms: 5 + -72x + 9x2 = 0 Solving 5 + -72x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + -8x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -8x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -8x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + -0.5555555556 -8x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -8x + x2 = -0.5555555556 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 = -0.5555555556 + 16 Reorder the terms: 16 + -8x + x2 = -0.5555555556 + 16 Combine like terms: -0.5555555556 + 16 = 15.4444444444 16 + -8x + x2 = 15.4444444444 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.4444444444 Calculate the square root of the right side: 3.929942041 Break this problem into two subproblems by setting (x + -4) equal to 3.929942041 and -3.929942041.Subproblem 1
x + -4 = 3.929942041 Simplifying x + -4 = 3.929942041 Reorder the terms: -4 + x = 3.929942041 Solving -4 + x = 3.929942041 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 = 3.929942041 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.929942041 + 4 x = 3.929942041 + 4 Combine like terms: 3.929942041 + 4 = 7.929942041 x = 7.929942041 Simplifying x = 7.929942041Subproblem 2
x + -4 = -3.929942041 Simplifying x + -4 = -3.929942041 Reorder the terms: -4 + x = -3.929942041 Solving -4 + x = -3.929942041 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 = -3.929942041 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.929942041 + 4 x = -3.929942041 + 4 Combine like terms: -3.929942041 + 4 = 0.070057959 x = 0.070057959 Simplifying x = 0.070057959Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.929942041, 0.070057959}
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