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Simplifying 7x2 + -21x + 4 = 0 Reorder the terms: 4 + -21x + 7x2 = 0 Solving 4 + -21x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + -3x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -3x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -3x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.5714285714 -3x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -3x + x2 = -0.5714285714 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.5714285714 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.5714285714 + 2.25 Combine like terms: -0.5714285714 + 2.25 = 1.6785714286 2.25 + -3x + x2 = 1.6785714286 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.6785714286 Calculate the square root of the right side: 1.295596939 Break this problem into two subproblems by setting (x + -1.5) equal to 1.295596939 and -1.295596939.Subproblem 1
x + -1.5 = 1.295596939 Simplifying x + -1.5 = 1.295596939 Reorder the terms: -1.5 + x = 1.295596939 Solving -1.5 + x = 1.295596939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.295596939 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.295596939 + 1.5 x = 1.295596939 + 1.5 Combine like terms: 1.295596939 + 1.5 = 2.795596939 x = 2.795596939 Simplifying x = 2.795596939Subproblem 2
x + -1.5 = -1.295596939 Simplifying x + -1.5 = -1.295596939 Reorder the terms: -1.5 + x = -1.295596939 Solving -1.5 + x = -1.295596939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.295596939 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.295596939 + 1.5 x = -1.295596939 + 1.5 Combine like terms: -1.295596939 + 1.5 = 0.204403061 x = 0.204403061 Simplifying x = 0.204403061Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.795596939, 0.204403061}
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