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Simplifying 4x2 + -24x + 19 = 0 Reorder the terms: 19 + -24x + 4x2 = 0 Solving 19 + -24x + 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'. 4.75 + -6x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + -6x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + -6x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + -6x + x2 = 0 + -4.75 -6x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 -6x + x2 = -4.75 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 = -4.75 + 9 Reorder the terms: 9 + -6x + x2 = -4.75 + 9 Combine like terms: -4.75 + 9 = 4.25 9 + -6x + x2 = 4.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -3) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -3 = 2.061552813 Simplifying x + -3 = 2.061552813 Reorder the terms: -3 + x = 2.061552813 Solving -3 + x = 2.061552813 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 = 2.061552813 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.061552813 + 3 x = 2.061552813 + 3 Combine like terms: 2.061552813 + 3 = 5.061552813 x = 5.061552813 Simplifying x = 5.061552813Subproblem 2
x + -3 = -2.061552813 Simplifying x + -3 = -2.061552813 Reorder the terms: -3 + x = -2.061552813 Solving -3 + x = -2.061552813 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 = -2.061552813 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.061552813 + 3 x = -2.061552813 + 3 Combine like terms: -2.061552813 + 3 = 0.938447187 x = 0.938447187 Simplifying x = 0.938447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.061552813, 0.938447187}
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