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Simplifying 4x2 + -19x + 5 = 0 Reorder the terms: 5 + -19x + 4x2 = 0 Solving 5 + -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'. 1.25 + -4.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.75x + x2 = 0 + -1.25 -4.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.75x + x2 = -1.25 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 = -1.25 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -1.25 + 5.640625 Combine like terms: -1.25 + 5.640625 = 4.390625 5.640625 + -4.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -2.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -2.375 = 2.095381827 Simplifying x + -2.375 = 2.095381827 Reorder the terms: -2.375 + x = 2.095381827 Solving -2.375 + x = 2.095381827 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 = 2.095381827 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 2.095381827 + 2.375 x = 2.095381827 + 2.375 Combine like terms: 2.095381827 + 2.375 = 4.470381827 x = 4.470381827 Simplifying x = 4.470381827Subproblem 2
x + -2.375 = -2.095381827 Simplifying x + -2.375 = -2.095381827 Reorder the terms: -2.375 + x = -2.095381827 Solving -2.375 + x = -2.095381827 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 = -2.095381827 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -2.095381827 + 2.375 x = -2.095381827 + 2.375 Combine like terms: -2.095381827 + 2.375 = 0.279618173 x = 0.279618173 Simplifying x = 0.279618173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.470381827, 0.279618173}
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