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Simplifying 30x2 + -12x = 3 Reorder the terms: -12x + 30x2 = 3 Solving -12x + 30x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -12x + 30x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -12x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -4x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -4x + 10x2)' equal to zero and attempt to solve: Simplifying -1 + -4x + 10x2 = 0 Solving -1 + -4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.1 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.4x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.4x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.4x + x2 = 0.0 + 0.1 -0.4x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -0.4x + x2 = 0.1 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.1 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.1 + 0.04 Combine like terms: 0.1 + 0.04 = 0.14 0.04 + -0.4x + x2 = 0.14 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.14 Calculate the square root of the right side: 0.374165739 Break this problem into two subproblems by setting (x + -0.2) equal to 0.374165739 and -0.374165739.Subproblem 1
x + -0.2 = 0.374165739 Simplifying x + -0.2 = 0.374165739 Reorder the terms: -0.2 + x = 0.374165739 Solving -0.2 + x = 0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.374165739 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.374165739 + 0.2 x = 0.374165739 + 0.2 Combine like terms: 0.374165739 + 0.2 = 0.574165739 x = 0.574165739 Simplifying x = 0.574165739Subproblem 2
x + -0.2 = -0.374165739 Simplifying x + -0.2 = -0.374165739 Reorder the terms: -0.2 + x = -0.374165739 Solving -0.2 + x = -0.374165739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.374165739 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.374165739 + 0.2 x = -0.374165739 + 0.2 Combine like terms: -0.374165739 + 0.2 = -0.174165739 x = -0.174165739 Simplifying x = -0.174165739Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.574165739, -0.174165739}Solution
x = {0.574165739, -0.174165739}
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