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Simplifying (7x2 + -3x + 14) + (2x2 + 7x + -75) = 0 Reorder the terms: (14 + -3x + 7x2) + (2x2 + 7x + -75) = 0 Remove parenthesis around (14 + -3x + 7x2) 14 + -3x + 7x2 + (2x2 + 7x + -75) = 0 Reorder the terms: 14 + -3x + 7x2 + (-75 + 7x + 2x2) = 0 Remove parenthesis around (-75 + 7x + 2x2) 14 + -3x + 7x2 + -75 + 7x + 2x2 = 0 Reorder the terms: 14 + -75 + -3x + 7x + 7x2 + 2x2 = 0 Combine like terms: 14 + -75 = -61 -61 + -3x + 7x + 7x2 + 2x2 = 0 Combine like terms: -3x + 7x = 4x -61 + 4x + 7x2 + 2x2 = 0 Combine like terms: 7x2 + 2x2 = 9x2 -61 + 4x + 9x2 = 0 Solving -61 + 4x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.777777778 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '6.777777778' to each side of the equation. -6.777777778 + 0.4444444444x + 6.777777778 + x2 = 0 + 6.777777778 Reorder the terms: -6.777777778 + 6.777777778 + 0.4444444444x + x2 = 0 + 6.777777778 Combine like terms: -6.777777778 + 6.777777778 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 6.777777778 0.4444444444x + x2 = 0 + 6.777777778 Combine like terms: 0 + 6.777777778 = 6.777777778 0.4444444444x + x2 = 6.777777778 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 6.777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 6.777777778 + 0.04938271604 Combine like terms: 6.777777778 + 0.04938271604 = 6.82716049404 0.04938271604 + 0.4444444444x + x2 = 6.82716049404 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 6.82716049404 Calculate the square root of the right side: 2.612883559 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 2.612883559 and -2.612883559.Subproblem 1
x + 0.2222222222 = 2.612883559 Simplifying x + 0.2222222222 = 2.612883559 Reorder the terms: 0.2222222222 + x = 2.612883559 Solving 0.2222222222 + x = 2.612883559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 2.612883559 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 2.612883559 + -0.2222222222 x = 2.612883559 + -0.2222222222 Combine like terms: 2.612883559 + -0.2222222222 = 2.3906613368 x = 2.3906613368 Simplifying x = 2.3906613368Subproblem 2
x + 0.2222222222 = -2.612883559 Simplifying x + 0.2222222222 = -2.612883559 Reorder the terms: 0.2222222222 + x = -2.612883559 Solving 0.2222222222 + x = -2.612883559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -2.612883559 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -2.612883559 + -0.2222222222 x = -2.612883559 + -0.2222222222 Combine like terms: -2.612883559 + -0.2222222222 = -2.8351057812 x = -2.8351057812 Simplifying x = -2.8351057812Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3906613368, -2.8351057812}
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