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Simplifying (15x2 + 7x + 19) + -1(16x2 + 18x + 6) = 0 Reorder the terms: (19 + 7x + 15x2) + -1(16x2 + 18x + 6) = 0 Remove parenthesis around (19 + 7x + 15x2) 19 + 7x + 15x2 + -1(16x2 + 18x + 6) = 0 Reorder the terms: 19 + 7x + 15x2 + -1(6 + 18x + 16x2) = 0 19 + 7x + 15x2 + (6 * -1 + 18x * -1 + 16x2 * -1) = 0 19 + 7x + 15x2 + (-6 + -18x + -16x2) = 0 Reorder the terms: 19 + -6 + 7x + -18x + 15x2 + -16x2 = 0 Combine like terms: 19 + -6 = 13 13 + 7x + -18x + 15x2 + -16x2 = 0 Combine like terms: 7x + -18x = -11x 13 + -11x + 15x2 + -16x2 = 0 Combine like terms: 15x2 + -16x2 = -1x2 13 + -11x + -1x2 = 0 Solving 13 + -11x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 11x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 11x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 11x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 11x + x2 = 0 + 13 11x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 11x + x2 = 13 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 13 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 13 + 30.25 Combine like terms: 13 + 30.25 = 43.25 30.25 + 11x + x2 = 43.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + 5.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + 5.5 = 6.576473219 Simplifying x + 5.5 = 6.576473219 Reorder the terms: 5.5 + x = 6.576473219 Solving 5.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.576473219 + -5.5 x = 6.576473219 + -5.5 Combine like terms: 6.576473219 + -5.5 = 1.076473219 x = 1.076473219 Simplifying x = 1.076473219Subproblem 2
x + 5.5 = -6.576473219 Simplifying x + 5.5 = -6.576473219 Reorder the terms: 5.5 + x = -6.576473219 Solving 5.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.576473219 + -5.5 x = -6.576473219 + -5.5 Combine like terms: -6.576473219 + -5.5 = -12.076473219 x = -12.076473219 Simplifying x = -12.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.076473219, -12.076473219}
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