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Simplifying 4x2 + -19x + 4 = 0 Reorder the terms: 4 + -19x + 4x2 = 0 Solving 4 + -19x + 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'. 1 + -4.75x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.75x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.75x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.75x + x2 = 0 + -1 -4.75x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.75x + x2 = -1 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = -1 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -1 + 5.640625 Combine like terms: -1 + 5.640625 = 4.640625 5.640625 + -4.75x + x2 = 4.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + -2.375) equal to 2.154210992 and -2.154210992.Subproblem 1
x + -2.375 = 2.154210992 Simplifying x + -2.375 = 2.154210992 Reorder the terms: -2.375 + x = 2.154210992 Solving -2.375 + x = 2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 2.154210992 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.154210992 + 2.375 x = 2.154210992 + 2.375 Combine like terms: 2.154210992 + 2.375 = 4.529210992 x = 4.529210992 Simplifying x = 4.529210992Subproblem 2
x + -2.375 = -2.154210992 Simplifying x + -2.375 = -2.154210992 Reorder the terms: -2.375 + x = -2.154210992 Solving -2.375 + x = -2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -2.154210992 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.154210992 + 2.375 x = -2.154210992 + 2.375 Combine like terms: -2.154210992 + 2.375 = 0.220789008 x = 0.220789008 Simplifying x = 0.220789008Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.529210992, 0.220789008}
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