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Simplifying (4x2 + -6) + (-2x2 + 19x) = 0 Reorder the terms: (-6 + 4x2) + (-2x2 + 19x) = 0 Remove parenthesis around (-6 + 4x2) -6 + 4x2 + (-2x2 + 19x) = 0 Reorder the terms: -6 + 4x2 + (19x + -2x2) = 0 Remove parenthesis around (19x + -2x2) -6 + 4x2 + 19x + -2x2 = 0 Reorder the terms: -6 + 19x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -6 + 19x + 2x2 = 0 Solving -6 + 19x + 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'. -3 + 9.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 9.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 9.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 9.5x + x2 = 0 + 3 9.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 9.5x + x2 = 3 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 3 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 3 + 22.5625 Combine like terms: 3 + 22.5625 = 25.5625 22.5625 + 9.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 4.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 4.75 = 5.055937104 Simplifying x + 4.75 = 5.055937104 Reorder the terms: 4.75 + x = 5.055937104 Solving 4.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 5.055937104 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 5.055937104 + -4.75 x = 5.055937104 + -4.75 Combine like terms: 5.055937104 + -4.75 = 0.305937104 x = 0.305937104 Simplifying x = 0.305937104Subproblem 2
x + 4.75 = -5.055937104 Simplifying x + 4.75 = -5.055937104 Reorder the terms: 4.75 + x = -5.055937104 Solving 4.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -5.055937104 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -5.055937104 + -4.75 x = -5.055937104 + -4.75 Combine like terms: -5.055937104 + -4.75 = -9.805937104 x = -9.805937104 Simplifying x = -9.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.305937104, -9.805937104}
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