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Simplifying (5x2 + -2x + -51) + (9x2 + 8x) = 0 Reorder the terms: (-51 + -2x + 5x2) + (9x2 + 8x) = 0 Remove parenthesis around (-51 + -2x + 5x2) -51 + -2x + 5x2 + (9x2 + 8x) = 0 Reorder the terms: -51 + -2x + 5x2 + (8x + 9x2) = 0 Remove parenthesis around (8x + 9x2) -51 + -2x + 5x2 + 8x + 9x2 = 0 Reorder the terms: -51 + -2x + 8x + 5x2 + 9x2 = 0 Combine like terms: -2x + 8x = 6x -51 + 6x + 5x2 + 9x2 = 0 Combine like terms: 5x2 + 9x2 = 14x2 -51 + 6x + 14x2 = 0 Solving -51 + 6x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -3.642857143 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '3.642857143' to each side of the equation. -3.642857143 + 0.4285714286x + 3.642857143 + x2 = 0 + 3.642857143 Reorder the terms: -3.642857143 + 3.642857143 + 0.4285714286x + x2 = 0 + 3.642857143 Combine like terms: -3.642857143 + 3.642857143 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + 3.642857143 0.4285714286x + x2 = 0 + 3.642857143 Combine like terms: 0 + 3.642857143 = 3.642857143 0.4285714286x + x2 = 3.642857143 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 3.642857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 3.642857143 + 0.04591836735 Combine like terms: 3.642857143 + 0.04591836735 = 3.68877551035 0.04591836735 + 0.4285714286x + x2 = 3.68877551035 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 3.68877551035 Calculate the square root of the right side: 1.920618523 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 1.920618523 and -1.920618523.Subproblem 1
x + 0.2142857143 = 1.920618523 Simplifying x + 0.2142857143 = 1.920618523 Reorder the terms: 0.2142857143 + x = 1.920618523 Solving 0.2142857143 + x = 1.920618523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 1.920618523 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 1.920618523 + -0.2142857143 x = 1.920618523 + -0.2142857143 Combine like terms: 1.920618523 + -0.2142857143 = 1.7063328087 x = 1.7063328087 Simplifying x = 1.7063328087Subproblem 2
x + 0.2142857143 = -1.920618523 Simplifying x + 0.2142857143 = -1.920618523 Reorder the terms: 0.2142857143 + x = -1.920618523 Solving 0.2142857143 + x = -1.920618523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -1.920618523 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -1.920618523 + -0.2142857143 x = -1.920618523 + -0.2142857143 Combine like terms: -1.920618523 + -0.2142857143 = -2.1349042373 x = -2.1349042373 Simplifying x = -2.1349042373Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7063328087, -2.1349042373}
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