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Simplifying (9x2 + -5x + 12) + (7x2 + 8x + -78) = 0 Reorder the terms: (12 + -5x + 9x2) + (7x2 + 8x + -78) = 0 Remove parenthesis around (12 + -5x + 9x2) 12 + -5x + 9x2 + (7x2 + 8x + -78) = 0 Reorder the terms: 12 + -5x + 9x2 + (-78 + 8x + 7x2) = 0 Remove parenthesis around (-78 + 8x + 7x2) 12 + -5x + 9x2 + -78 + 8x + 7x2 = 0 Reorder the terms: 12 + -78 + -5x + 8x + 9x2 + 7x2 = 0 Combine like terms: 12 + -78 = -66 -66 + -5x + 8x + 9x2 + 7x2 = 0 Combine like terms: -5x + 8x = 3x -66 + 3x + 9x2 + 7x2 = 0 Combine like terms: 9x2 + 7x2 = 16x2 -66 + 3x + 16x2 = 0 Solving -66 + 3x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.125 + 0.1875x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + 0.1875x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + 0.1875x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + 0.1875x + x2 = 0 + 4.125 0.1875x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 0.1875x + x2 = 4.125 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 4.125 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 4.125 + 0.0087890625 Combine like terms: 4.125 + 0.0087890625 = 4.1337890625 0.0087890625 + 0.1875x + x2 = 4.1337890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 4.1337890625 Calculate the square root of the right side: 2.033172167 Break this problem into two subproblems by setting (x + 0.09375) equal to 2.033172167 and -2.033172167.Subproblem 1
x + 0.09375 = 2.033172167 Simplifying x + 0.09375 = 2.033172167 Reorder the terms: 0.09375 + x = 2.033172167 Solving 0.09375 + x = 2.033172167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 2.033172167 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 2.033172167 + -0.09375 x = 2.033172167 + -0.09375 Combine like terms: 2.033172167 + -0.09375 = 1.939422167 x = 1.939422167 Simplifying x = 1.939422167Subproblem 2
x + 0.09375 = -2.033172167 Simplifying x + 0.09375 = -2.033172167 Reorder the terms: 0.09375 + x = -2.033172167 Solving 0.09375 + x = -2.033172167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -2.033172167 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -2.033172167 + -0.09375 x = -2.033172167 + -0.09375 Combine like terms: -2.033172167 + -0.09375 = -2.126922167 x = -2.126922167 Simplifying x = -2.126922167Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.939422167, -2.126922167}
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