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Simplifying 5x2 + -30x + 38 = 0 Reorder the terms: 38 + -30x + 5x2 = 0 Solving 38 + -30x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.6 + -6x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + -6x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + -6x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + -6x + x2 = 0 + -7.6 -6x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 -6x + x2 = -7.6 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7.6 + 9 Reorder the terms: 9 + -6x + x2 = -7.6 + 9 Combine like terms: -7.6 + 9 = 1.4 9 + -6x + x2 = 1.4 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (x + -3) equal to 1.183215957 and -1.183215957.Subproblem 1
x + -3 = 1.183215957 Simplifying x + -3 = 1.183215957 Reorder the terms: -3 + x = 1.183215957 Solving -3 + x = 1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.183215957 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.183215957 + 3 x = 1.183215957 + 3 Combine like terms: 1.183215957 + 3 = 4.183215957 x = 4.183215957 Simplifying x = 4.183215957Subproblem 2
x + -3 = -1.183215957 Simplifying x + -3 = -1.183215957 Reorder the terms: -3 + x = -1.183215957 Solving -3 + x = -1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.183215957 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.183215957 + 3 x = -1.183215957 + 3 Combine like terms: -1.183215957 + 3 = 1.816784043 x = 1.816784043 Simplifying x = 1.816784043Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.183215957, 1.816784043}
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