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Simplifying 3x + 3(70x) * x = 2010 Remove parenthesis around (70x) 3x + 3 * 70x * x = 2010 Multiply 3 * 70 3x + 210x * x = 2010 Multiply x * x 3x + 210x2 = 2010 Solving 3x + 210x2 = 2010 Solving for variable 'x'. Reorder the terms: -2010 + 3x + 210x2 = 2010 + -2010 Combine like terms: 2010 + -2010 = 0 -2010 + 3x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-670 + x + 70x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-670 + x + 70x2)' equal to zero and attempt to solve: Simplifying -670 + x + 70x2 = 0 Solving -670 + x + 70x2 = 0 Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -9.571428571 + 0.01428571429x + x2 = 0.0 Move the constant term to the right: Add '9.571428571' to each side of the equation. -9.571428571 + 0.01428571429x + 9.571428571 + x2 = 0.0 + 9.571428571 Reorder the terms: -9.571428571 + 9.571428571 + 0.01428571429x + x2 = 0.0 + 9.571428571 Combine like terms: -9.571428571 + 9.571428571 = 0.000000000 0.000000000 + 0.01428571429x + x2 = 0.0 + 9.571428571 0.01428571429x + x2 = 0.0 + 9.571428571 Combine like terms: 0.0 + 9.571428571 = 9.571428571 0.01428571429x + x2 = 9.571428571 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01428571429x + 0.25 + x2 = 9.571428571 + 0.25 Reorder the terms: 0.25 + 0.01428571429x + x2 = 9.571428571 + 0.25 Combine like terms: 9.571428571 + 0.25 = 9.821428571 0.25 + 0.01428571429x + x2 = 9.821428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.821428571 Calculate the square root of the right side: 3.133915853 Break this problem into two subproblems by setting (x + 0.5) equal to 3.133915853 and -3.133915853.Subproblem 1
x + 0.5 = 3.133915853 Simplifying x + 0.5 = 3.133915853 Reorder the terms: 0.5 + x = 3.133915853 Solving 0.5 + x = 3.133915853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.133915853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.133915853 + -0.5 x = 3.133915853 + -0.5 Combine like terms: 3.133915853 + -0.5 = 2.633915853 x = 2.633915853 Simplifying x = 2.633915853Subproblem 2
x + 0.5 = -3.133915853 Simplifying x + 0.5 = -3.133915853 Reorder the terms: 0.5 + x = -3.133915853 Solving 0.5 + x = -3.133915853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.133915853 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.133915853 + -0.5 x = -3.133915853 + -0.5 Combine like terms: -3.133915853 + -0.5 = -3.633915853 x = -3.633915853 Simplifying x = -3.633915853Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.633915853, -3.633915853}Solution
x = {2.633915853, -3.633915853}
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