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Simplifying (6x2 + 19x + 2) + (-4x2 + 10x + -11) = 0 Reorder the terms: (2 + 19x + 6x2) + (-4x2 + 10x + -11) = 0 Remove parenthesis around (2 + 19x + 6x2) 2 + 19x + 6x2 + (-4x2 + 10x + -11) = 0 Reorder the terms: 2 + 19x + 6x2 + (-11 + 10x + -4x2) = 0 Remove parenthesis around (-11 + 10x + -4x2) 2 + 19x + 6x2 + -11 + 10x + -4x2 = 0 Reorder the terms: 2 + -11 + 19x + 10x + 6x2 + -4x2 = 0 Combine like terms: 2 + -11 = -9 -9 + 19x + 10x + 6x2 + -4x2 = 0 Combine like terms: 19x + 10x = 29x -9 + 29x + 6x2 + -4x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 -9 + 29x + 2x2 = 0 Solving -9 + 29x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 14.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 14.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 14.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 14.5x + x2 = 0 + 4.5 14.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 14.5x + x2 = 4.5 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 4.5 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 4.5 + 52.5625 Combine like terms: 4.5 + 52.5625 = 57.0625 52.5625 + 14.5x + x2 = 57.0625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 57.0625 Calculate the square root of the right side: 7.553972465 Break this problem into two subproblems by setting (x + 7.25) equal to 7.553972465 and -7.553972465.Subproblem 1
x + 7.25 = 7.553972465 Simplifying x + 7.25 = 7.553972465 Reorder the terms: 7.25 + x = 7.553972465 Solving 7.25 + x = 7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 7.553972465 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.553972465 + -7.25 x = 7.553972465 + -7.25 Combine like terms: 7.553972465 + -7.25 = 0.303972465 x = 0.303972465 Simplifying x = 0.303972465Subproblem 2
x + 7.25 = -7.553972465 Simplifying x + 7.25 = -7.553972465 Reorder the terms: 7.25 + x = -7.553972465 Solving 7.25 + x = -7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -7.553972465 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.553972465 + -7.25 x = -7.553972465 + -7.25 Combine like terms: -7.553972465 + -7.25 = -14.803972465 x = -14.803972465 Simplifying x = -14.803972465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.303972465, -14.803972465}
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