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Simplifying -10x + 20 + -45x2 = 0 Reorder the terms: 20 + -10x + -45x2 = 0 Solving 20 + -10x + -45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(4 + -2x + -9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -2x + -9x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + -9x2 = 0 Solving 4 + -2x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.4444444444 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.2222222222x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.2222222222x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + 0.4444444444 0.2222222222x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.2222222222x + x2 = 0.4444444444 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 0.4444444444 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.4444444444 + 0.01234567901 Combine like terms: 0.4444444444 + 0.01234567901 = 0.45679012341 0.01234567901 + 0.2222222222x + x2 = 0.45679012341 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.45679012341 Calculate the square root of the right side: 0.675862503 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.675862503 and -0.675862503.Subproblem 1
x + 0.1111111111 = 0.675862503 Simplifying x + 0.1111111111 = 0.675862503 Reorder the terms: 0.1111111111 + x = 0.675862503 Solving 0.1111111111 + x = 0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.675862503 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.675862503 + -0.1111111111 x = 0.675862503 + -0.1111111111 Combine like terms: 0.675862503 + -0.1111111111 = 0.5647513919 x = 0.5647513919 Simplifying x = 0.5647513919Subproblem 2
x + 0.1111111111 = -0.675862503 Simplifying x + 0.1111111111 = -0.675862503 Reorder the terms: 0.1111111111 + x = -0.675862503 Solving 0.1111111111 + x = -0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.675862503 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.675862503 + -0.1111111111 x = -0.675862503 + -0.1111111111 Combine like terms: -0.675862503 + -0.1111111111 = -0.7869736141 x = -0.7869736141 Simplifying x = -0.7869736141Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5647513919, -0.7869736141}Solution
x = {0.5647513919, -0.7869736141}
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