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Simplifying 4x2 + -30x + 1 = 0 Reorder the terms: 1 + -30x + 4x2 = 0 Solving 1 + -30x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -7.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -7.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -7.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -7.5x + x2 = 0 + -0.25 -7.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -7.5x + x2 = -0.25 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -0.25 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -0.25 + 14.0625 Combine like terms: -0.25 + 14.0625 = 13.8125 14.0625 + -7.5x + x2 = 13.8125 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (x + -3.75) equal to 3.716517187 and -3.716517187.Subproblem 1
x + -3.75 = 3.716517187 Simplifying x + -3.75 = 3.716517187 Reorder the terms: -3.75 + x = 3.716517187 Solving -3.75 + x = 3.716517187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.716517187 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.716517187 + 3.75 x = 3.716517187 + 3.75 Combine like terms: 3.716517187 + 3.75 = 7.466517187 x = 7.466517187 Simplifying x = 7.466517187Subproblem 2
x + -3.75 = -3.716517187 Simplifying x + -3.75 = -3.716517187 Reorder the terms: -3.75 + x = -3.716517187 Solving -3.75 + x = -3.716517187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.716517187 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.716517187 + 3.75 x = -3.716517187 + 3.75 Combine like terms: -3.716517187 + 3.75 = 0.033482813 x = 0.033482813 Simplifying x = 0.033482813Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.466517187, 0.033482813}
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