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Simplifying 9x2 + 8x + 1 = 158 Reorder the terms: 1 + 8x + 9x2 = 158 Solving 1 + 8x + 9x2 = 158 Solving for variable 'x'. Reorder the terms: 1 + -158 + 8x + 9x2 = 158 + -158 Combine like terms: 1 + -158 = -157 -157 + 8x + 9x2 = 158 + -158 Combine like terms: 158 + -158 = 0 -157 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -17.44444444 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '17.44444444' to each side of the equation. -17.44444444 + 0.8888888889x + 17.44444444 + x2 = 0 + 17.44444444 Reorder the terms: -17.44444444 + 17.44444444 + 0.8888888889x + x2 = 0 + 17.44444444 Combine like terms: -17.44444444 + 17.44444444 = 0.00000000 0.00000000 + 0.8888888889x + x2 = 0 + 17.44444444 0.8888888889x + x2 = 0 + 17.44444444 Combine like terms: 0 + 17.44444444 = 17.44444444 0.8888888889x + x2 = 17.44444444 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 17.44444444 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 17.44444444 + 0.1975308642 Combine like terms: 17.44444444 + 0.1975308642 = 17.6419753042 0.1975308642 + 0.8888888889x + x2 = 17.6419753042 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 17.6419753042 Calculate the square root of the right side: 4.200235149 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 4.200235149 and -4.200235149.Subproblem 1
x + 0.4444444445 = 4.200235149 Simplifying x + 0.4444444445 = 4.200235149 Reorder the terms: 0.4444444445 + x = 4.200235149 Solving 0.4444444445 + x = 4.200235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 4.200235149 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 4.200235149 + -0.4444444445 x = 4.200235149 + -0.4444444445 Combine like terms: 4.200235149 + -0.4444444445 = 3.7557907045 x = 3.7557907045 Simplifying x = 3.7557907045Subproblem 2
x + 0.4444444445 = -4.200235149 Simplifying x + 0.4444444445 = -4.200235149 Reorder the terms: 0.4444444445 + x = -4.200235149 Solving 0.4444444445 + x = -4.200235149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -4.200235149 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -4.200235149 + -0.4444444445 x = -4.200235149 + -0.4444444445 Combine like terms: -4.200235149 + -0.4444444445 = -4.6446795935 x = -4.6446795935 Simplifying x = -4.6446795935Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.7557907045, -4.6446795935}
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