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Simplifying x2 + 19x = 850 Reorder the terms: 19x + x2 = 850 Solving 19x + x2 = 850 Solving for variable 'x'. Reorder the terms: -850 + 19x + x2 = 850 + -850 Combine like terms: 850 + -850 = 0 -850 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '850' to each side of the equation. -850 + 19x + 850 + x2 = 0 + 850 Reorder the terms: -850 + 850 + 19x + x2 = 0 + 850 Combine like terms: -850 + 850 = 0 0 + 19x + x2 = 0 + 850 19x + x2 = 0 + 850 Combine like terms: 0 + 850 = 850 19x + x2 = 850 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 850 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 850 + 90.25 Combine like terms: 850 + 90.25 = 940.25 90.25 + 19x + x2 = 940.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 940.25 Calculate the square root of the right side: 30.663496213 Break this problem into two subproblems by setting (x + 9.5) equal to 30.663496213 and -30.663496213.Subproblem 1
x + 9.5 = 30.663496213 Simplifying x + 9.5 = 30.663496213 Reorder the terms: 9.5 + x = 30.663496213 Solving 9.5 + x = 30.663496213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 30.663496213 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 30.663496213 + -9.5 x = 30.663496213 + -9.5 Combine like terms: 30.663496213 + -9.5 = 21.163496213 x = 21.163496213 Simplifying x = 21.163496213Subproblem 2
x + 9.5 = -30.663496213 Simplifying x + 9.5 = -30.663496213 Reorder the terms: 9.5 + x = -30.663496213 Solving 9.5 + x = -30.663496213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -30.663496213 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -30.663496213 + -9.5 x = -30.663496213 + -9.5 Combine like terms: -30.663496213 + -9.5 = -40.163496213 x = -40.163496213 Simplifying x = -40.163496213Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.163496213, -40.163496213}
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