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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 = -0.938447187 x = -0.938447187 Simplifying x = -0.938447187Subproblem 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 = -5.061552813 x = -5.061552813 Simplifying x = -5.061552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.938447187, -5.061552813}
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