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Simplifying 21x2 + -9x + -4 = 0 Reorder the terms: -4 + -9x + 21x2 = 0 Solving -4 + -9x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.1904761905 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.1904761905' to each side of the equation. -0.1904761905 + -0.4285714286x + 0.1904761905 + x2 = 0 + 0.1904761905 Reorder the terms: -0.1904761905 + 0.1904761905 + -0.4285714286x + x2 = 0 + 0.1904761905 Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000 0.0000000000 + -0.4285714286x + x2 = 0 + 0.1904761905 -0.4285714286x + x2 = 0 + 0.1904761905 Combine like terms: 0 + 0.1904761905 = 0.1904761905 -0.4285714286x + x2 = 0.1904761905 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 = 0.1904761905 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 0.1904761905 + 0.04591836735 Combine like terms: 0.1904761905 + 0.04591836735 = 0.23639455785 0.04591836735 + -0.4285714286x + x2 = 0.23639455785 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.23639455785 Calculate the square root of the right side: 0.486204235 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.486204235 and -0.486204235.Subproblem 1
x + -0.2142857143 = 0.486204235 Simplifying x + -0.2142857143 = 0.486204235 Reorder the terms: -0.2142857143 + x = 0.486204235 Solving -0.2142857143 + x = 0.486204235 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 = 0.486204235 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.486204235 + 0.2142857143 x = 0.486204235 + 0.2142857143 Combine like terms: 0.486204235 + 0.2142857143 = 0.7004899493 x = 0.7004899493 Simplifying x = 0.7004899493Subproblem 2
x + -0.2142857143 = -0.486204235 Simplifying x + -0.2142857143 = -0.486204235 Reorder the terms: -0.2142857143 + x = -0.486204235 Solving -0.2142857143 + x = -0.486204235 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 = -0.486204235 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.486204235 + 0.2142857143 x = -0.486204235 + 0.2142857143 Combine like terms: -0.486204235 + 0.2142857143 = -0.2719185207 x = -0.2719185207 Simplifying x = -0.2719185207Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7004899493, -0.2719185207}
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