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Simplifying 4x2 + -19x + 9 = 0 Reorder the terms: 9 + -19x + 4x2 = 0 Solving 9 + -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'. 2.25 + -4.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -4.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -4.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -4.75x + x2 = 0 + -2.25 -4.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -4.75x + x2 = -2.25 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 = -2.25 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -2.25 + 5.640625 Combine like terms: -2.25 + 5.640625 = 3.390625 5.640625 + -4.75x + x2 = 3.390625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -2.375) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -2.375 = 1.841364983 Simplifying x + -2.375 = 1.841364983 Reorder the terms: -2.375 + x = 1.841364983 Solving -2.375 + x = 1.841364983 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 = 1.841364983 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 1.841364983 + 2.375 x = 1.841364983 + 2.375 Combine like terms: 1.841364983 + 2.375 = 4.216364983 x = 4.216364983 Simplifying x = 4.216364983Subproblem 2
x + -2.375 = -1.841364983 Simplifying x + -2.375 = -1.841364983 Reorder the terms: -2.375 + x = -1.841364983 Solving -2.375 + x = -1.841364983 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 = -1.841364983 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -1.841364983 + 2.375 x = -1.841364983 + 2.375 Combine like terms: -1.841364983 + 2.375 = 0.533635017 x = 0.533635017 Simplifying x = 0.533635017Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.216364983, 0.533635017}
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