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Simplifying 9x2 + -90x + 145 = 0 Reorder the terms: 145 + -90x + 9x2 = 0 Solving 145 + -90x + 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'. 16.11111111 + -10x + x2 = 0 Move the constant term to the right: Add '-16.11111111' to each side of the equation. 16.11111111 + -10x + -16.11111111 + x2 = 0 + -16.11111111 Reorder the terms: 16.11111111 + -16.11111111 + -10x + x2 = 0 + -16.11111111 Combine like terms: 16.11111111 + -16.11111111 = 0.00000000 0.00000000 + -10x + x2 = 0 + -16.11111111 -10x + x2 = 0 + -16.11111111 Combine like terms: 0 + -16.11111111 = -16.11111111 -10x + x2 = -16.11111111 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -16.11111111 + 25 Reorder the terms: 25 + -10x + x2 = -16.11111111 + 25 Combine like terms: -16.11111111 + 25 = 8.88888889 25 + -10x + x2 = 8.88888889 Factor a perfect square on the left side: (x + -5)(x + -5) = 8.88888889 Calculate the square root of the right side: 2.98142397 Break this problem into two subproblems by setting (x + -5) equal to 2.98142397 and -2.98142397.Subproblem 1
x + -5 = 2.98142397 Simplifying x + -5 = 2.98142397 Reorder the terms: -5 + x = 2.98142397 Solving -5 + x = 2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.98142397 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.98142397 + 5 x = 2.98142397 + 5 Combine like terms: 2.98142397 + 5 = 7.98142397 x = 7.98142397 Simplifying x = 7.98142397Subproblem 2
x + -5 = -2.98142397 Simplifying x + -5 = -2.98142397 Reorder the terms: -5 + x = -2.98142397 Solving -5 + x = -2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.98142397 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.98142397 + 5 x = -2.98142397 + 5 Combine like terms: -2.98142397 + 5 = 2.01857603 x = 2.01857603 Simplifying x = 2.01857603Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.98142397, 2.01857603}
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