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Simplifying (8x2 + -4x + 11) + (9x2 + 8x + -78) = 0 Reorder the terms: (11 + -4x + 8x2) + (9x2 + 8x + -78) = 0 Remove parenthesis around (11 + -4x + 8x2) 11 + -4x + 8x2 + (9x2 + 8x + -78) = 0 Reorder the terms: 11 + -4x + 8x2 + (-78 + 8x + 9x2) = 0 Remove parenthesis around (-78 + 8x + 9x2) 11 + -4x + 8x2 + -78 + 8x + 9x2 = 0 Reorder the terms: 11 + -78 + -4x + 8x + 8x2 + 9x2 = 0 Combine like terms: 11 + -78 = -67 -67 + -4x + 8x + 8x2 + 9x2 = 0 Combine like terms: -4x + 8x = 4x -67 + 4x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 -67 + 4x + 17x2 = 0 Solving -67 + 4x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.941176471 + 0.2352941176x + x2 = 0 Move the constant term to the right: Add '3.941176471' to each side of the equation. -3.941176471 + 0.2352941176x + 3.941176471 + x2 = 0 + 3.941176471 Reorder the terms: -3.941176471 + 3.941176471 + 0.2352941176x + x2 = 0 + 3.941176471 Combine like terms: -3.941176471 + 3.941176471 = 0.000000000 0.000000000 + 0.2352941176x + x2 = 0 + 3.941176471 0.2352941176x + x2 = 0 + 3.941176471 Combine like terms: 0 + 3.941176471 = 3.941176471 0.2352941176x + x2 = 3.941176471 The x term is 0.2352941176x. Take half its coefficient (0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. 0.2352941176x + 0.01384083044 + x2 = 3.941176471 + 0.01384083044 Reorder the terms: 0.01384083044 + 0.2352941176x + x2 = 3.941176471 + 0.01384083044 Combine like terms: 3.941176471 + 0.01384083044 = 3.95501730144 0.01384083044 + 0.2352941176x + x2 = 3.95501730144 Factor a perfect square on the left side: (x + 0.1176470588)(x + 0.1176470588) = 3.95501730144 Calculate the square root of the right side: 1.98872253 Break this problem into two subproblems by setting (x + 0.1176470588) equal to 1.98872253 and -1.98872253.Subproblem 1
x + 0.1176470588 = 1.98872253 Simplifying x + 0.1176470588 = 1.98872253 Reorder the terms: 0.1176470588 + x = 1.98872253 Solving 0.1176470588 + x = 1.98872253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = 1.98872253 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = 1.98872253 + -0.1176470588 x = 1.98872253 + -0.1176470588 Combine like terms: 1.98872253 + -0.1176470588 = 1.8710754712 x = 1.8710754712 Simplifying x = 1.8710754712Subproblem 2
x + 0.1176470588 = -1.98872253 Simplifying x + 0.1176470588 = -1.98872253 Reorder the terms: 0.1176470588 + x = -1.98872253 Solving 0.1176470588 + x = -1.98872253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = -1.98872253 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = -1.98872253 + -0.1176470588 x = -1.98872253 + -0.1176470588 Combine like terms: -1.98872253 + -0.1176470588 = -2.1063695888 x = -2.1063695888 Simplifying x = -2.1063695888Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8710754712, -2.1063695888}
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