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Simplifying x2 + 9x = 640 Reorder the terms: 9x + x2 = 640 Solving 9x + x2 = 640 Solving for variable 'x'. Reorder the terms: -640 + 9x + x2 = 640 + -640 Combine like terms: 640 + -640 = 0 -640 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '640' to each side of the equation. -640 + 9x + 640 + x2 = 0 + 640 Reorder the terms: -640 + 640 + 9x + x2 = 0 + 640 Combine like terms: -640 + 640 = 0 0 + 9x + x2 = 0 + 640 9x + x2 = 0 + 640 Combine like terms: 0 + 640 = 640 9x + x2 = 640 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 640 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 640 + 20.25 Combine like terms: 640 + 20.25 = 660.25 20.25 + 9x + x2 = 660.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 660.25 Calculate the square root of the right side: 25.695330315 Break this problem into two subproblems by setting (x + 4.5) equal to 25.695330315 and -25.695330315.Subproblem 1
x + 4.5 = 25.695330315 Simplifying x + 4.5 = 25.695330315 Reorder the terms: 4.5 + x = 25.695330315 Solving 4.5 + x = 25.695330315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 25.695330315 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 25.695330315 + -4.5 x = 25.695330315 + -4.5 Combine like terms: 25.695330315 + -4.5 = 21.195330315 x = 21.195330315 Simplifying x = 21.195330315Subproblem 2
x + 4.5 = -25.695330315 Simplifying x + 4.5 = -25.695330315 Reorder the terms: 4.5 + x = -25.695330315 Solving 4.5 + x = -25.695330315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -25.695330315 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -25.695330315 + -4.5 x = -25.695330315 + -4.5 Combine like terms: -25.695330315 + -4.5 = -30.195330315 x = -30.195330315 Simplifying x = -30.195330315Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.195330315, -30.195330315}
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