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Simplifying 42x2 + 45x + -3 = 0 Reorder the terms: -3 + 45x + 42x2 = 0 Solving -3 + 45x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 15x + 14x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 15x + 14x2)' equal to zero and attempt to solve: Simplifying -1 + 15x + 14x2 = 0 Solving -1 + 15x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.07142857143 + 1.071428571x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + 1.071428571x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + 1.071428571x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + 1.071428571x + x2 = 0 + 0.07142857143 1.071428571x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 1.071428571x + x2 = 0.07142857143 The x term is 1.071428571x. Take half its coefficient (0.5357142855). Square it (0.2869897957) and add it to both sides. Add '0.2869897957' to each side of the equation. 1.071428571x + 0.2869897957 + x2 = 0.07142857143 + 0.2869897957 Reorder the terms: 0.2869897957 + 1.071428571x + x2 = 0.07142857143 + 0.2869897957 Combine like terms: 0.07142857143 + 0.2869897957 = 0.35841836713 0.2869897957 + 1.071428571x + x2 = 0.35841836713 Factor a perfect square on the left side: (x + 0.5357142855)(x + 0.5357142855) = 0.35841836713 Calculate the square root of the right side: 0.598680522 Break this problem into two subproblems by setting (x + 0.5357142855) equal to 0.598680522 and -0.598680522.Subproblem 1
x + 0.5357142855 = 0.598680522 Simplifying x + 0.5357142855 = 0.598680522 Reorder the terms: 0.5357142855 + x = 0.598680522 Solving 0.5357142855 + x = 0.598680522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = 0.598680522 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = 0.598680522 + -0.5357142855 x = 0.598680522 + -0.5357142855 Combine like terms: 0.598680522 + -0.5357142855 = 0.0629662365 x = 0.0629662365 Simplifying x = 0.0629662365Subproblem 2
x + 0.5357142855 = -0.598680522 Simplifying x + 0.5357142855 = -0.598680522 Reorder the terms: 0.5357142855 + x = -0.598680522 Solving 0.5357142855 + x = -0.598680522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5357142855' to each side of the equation. 0.5357142855 + -0.5357142855 + x = -0.598680522 + -0.5357142855 Combine like terms: 0.5357142855 + -0.5357142855 = 0.0000000000 0.0000000000 + x = -0.598680522 + -0.5357142855 x = -0.598680522 + -0.5357142855 Combine like terms: -0.598680522 + -0.5357142855 = -1.1343948075 x = -1.1343948075 Simplifying x = -1.1343948075Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0629662365, -1.1343948075}Solution
x = {0.0629662365, -1.1343948075}
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