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Simplifying 7x2 + 144x + 90 = 0 Reorder the terms: 90 + 144x + 7x2 = 0 Solving 90 + 144x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 12.85714286 + 20.57142857x + x2 = 0 Move the constant term to the right: Add '-12.85714286' to each side of the equation. 12.85714286 + 20.57142857x + -12.85714286 + x2 = 0 + -12.85714286 Reorder the terms: 12.85714286 + -12.85714286 + 20.57142857x + x2 = 0 + -12.85714286 Combine like terms: 12.85714286 + -12.85714286 = 0.00000000 0.00000000 + 20.57142857x + x2 = 0 + -12.85714286 20.57142857x + x2 = 0 + -12.85714286 Combine like terms: 0 + -12.85714286 = -12.85714286 20.57142857x + x2 = -12.85714286 The x term is 20.57142857x. Take half its coefficient (10.28571429). Square it (105.7959185) and add it to both sides. Add '105.7959185' to each side of the equation. 20.57142857x + 105.7959185 + x2 = -12.85714286 + 105.7959185 Reorder the terms: 105.7959185 + 20.57142857x + x2 = -12.85714286 + 105.7959185 Combine like terms: -12.85714286 + 105.7959185 = 92.93877564 105.7959185 + 20.57142857x + x2 = 92.93877564 Factor a perfect square on the left side: (x + 10.28571429)(x + 10.28571429) = 92.93877564 Calculate the square root of the right side: 9.640475903 Break this problem into two subproblems by setting (x + 10.28571429) equal to 9.640475903 and -9.640475903.Subproblem 1
x + 10.28571429 = 9.640475903 Simplifying x + 10.28571429 = 9.640475903 Reorder the terms: 10.28571429 + x = 9.640475903 Solving 10.28571429 + x = 9.640475903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.28571429' to each side of the equation. 10.28571429 + -10.28571429 + x = 9.640475903 + -10.28571429 Combine like terms: 10.28571429 + -10.28571429 = 0.00000000 0.00000000 + x = 9.640475903 + -10.28571429 x = 9.640475903 + -10.28571429 Combine like terms: 9.640475903 + -10.28571429 = -0.645238387 x = -0.645238387 Simplifying x = -0.645238387Subproblem 2
x + 10.28571429 = -9.640475903 Simplifying x + 10.28571429 = -9.640475903 Reorder the terms: 10.28571429 + x = -9.640475903 Solving 10.28571429 + x = -9.640475903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.28571429' to each side of the equation. 10.28571429 + -10.28571429 + x = -9.640475903 + -10.28571429 Combine like terms: 10.28571429 + -10.28571429 = 0.00000000 0.00000000 + x = -9.640475903 + -10.28571429 x = -9.640475903 + -10.28571429 Combine like terms: -9.640475903 + -10.28571429 = -19.926190193 x = -19.926190193 Simplifying x = -19.926190193Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.645238387, -19.926190193}
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