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Simplifying (8x2 + -7x + 2) + (3x2 + -9x + -6) = 0 Reorder the terms: (2 + -7x + 8x2) + (3x2 + -9x + -6) = 0 Remove parenthesis around (2 + -7x + 8x2) 2 + -7x + 8x2 + (3x2 + -9x + -6) = 0 Reorder the terms: 2 + -7x + 8x2 + (-6 + -9x + 3x2) = 0 Remove parenthesis around (-6 + -9x + 3x2) 2 + -7x + 8x2 + -6 + -9x + 3x2 = 0 Reorder the terms: 2 + -6 + -7x + -9x + 8x2 + 3x2 = 0 Combine like terms: 2 + -6 = -4 -4 + -7x + -9x + 8x2 + 3x2 = 0 Combine like terms: -7x + -9x = -16x -4 + -16x + 8x2 + 3x2 = 0 Combine like terms: 8x2 + 3x2 = 11x2 -4 + -16x + 11x2 = 0 Solving -4 + -16x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + -1.454545455x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -1.454545455x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -1.454545455x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -1.454545455x + x2 = 0 + 0.3636363636 -1.454545455x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -1.454545455x + x2 = 0.3636363636 The x term is -1.454545455x. Take half its coefficient (-0.7272727275). Square it (0.5289256202) and add it to both sides. Add '0.5289256202' to each side of the equation. -1.454545455x + 0.5289256202 + x2 = 0.3636363636 + 0.5289256202 Reorder the terms: 0.5289256202 + -1.454545455x + x2 = 0.3636363636 + 0.5289256202 Combine like terms: 0.3636363636 + 0.5289256202 = 0.8925619838 0.5289256202 + -1.454545455x + x2 = 0.8925619838 Factor a perfect square on the left side: (x + -0.7272727275)(x + -0.7272727275) = 0.8925619838 Calculate the square root of the right side: 0.944754986 Break this problem into two subproblems by setting (x + -0.7272727275) equal to 0.944754986 and -0.944754986.Subproblem 1
x + -0.7272727275 = 0.944754986 Simplifying x + -0.7272727275 = 0.944754986 Reorder the terms: -0.7272727275 + x = 0.944754986 Solving -0.7272727275 + x = 0.944754986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = 0.944754986 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = 0.944754986 + 0.7272727275 x = 0.944754986 + 0.7272727275 Combine like terms: 0.944754986 + 0.7272727275 = 1.6720277135 x = 1.6720277135 Simplifying x = 1.6720277135Subproblem 2
x + -0.7272727275 = -0.944754986 Simplifying x + -0.7272727275 = -0.944754986 Reorder the terms: -0.7272727275 + x = -0.944754986 Solving -0.7272727275 + x = -0.944754986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7272727275' to each side of the equation. -0.7272727275 + 0.7272727275 + x = -0.944754986 + 0.7272727275 Combine like terms: -0.7272727275 + 0.7272727275 = 0.0000000000 0.0000000000 + x = -0.944754986 + 0.7272727275 x = -0.944754986 + 0.7272727275 Combine like terms: -0.944754986 + 0.7272727275 = -0.2174822585 x = -0.2174822585 Simplifying x = -0.2174822585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6720277135, -0.2174822585}
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