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Simplifying 5x2 + -39x + 29 = 0 Reorder the terms: 29 + -39x + 5x2 = 0 Solving 29 + -39x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.8 + -7.8x + x2 = 0 Move the constant term to the right: Add '-5.8' to each side of the equation. 5.8 + -7.8x + -5.8 + x2 = 0 + -5.8 Reorder the terms: 5.8 + -5.8 + -7.8x + x2 = 0 + -5.8 Combine like terms: 5.8 + -5.8 = 0.0 0.0 + -7.8x + x2 = 0 + -5.8 -7.8x + x2 = 0 + -5.8 Combine like terms: 0 + -5.8 = -5.8 -7.8x + x2 = -5.8 The x term is -7.8x. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8x + 15.21 + x2 = -5.8 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = -5.8 + 15.21 Combine like terms: -5.8 + 15.21 = 9.41 15.21 + -7.8x + x2 = 9.41 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 9.41 Calculate the square root of the right side: 3.06757233 Break this problem into two subproblems by setting (x + -3.9) equal to 3.06757233 and -3.06757233.Subproblem 1
x + -3.9 = 3.06757233 Simplifying x + -3.9 = 3.06757233 Reorder the terms: -3.9 + x = 3.06757233 Solving -3.9 + x = 3.06757233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = 3.06757233 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 3.06757233 + 3.9 x = 3.06757233 + 3.9 Combine like terms: 3.06757233 + 3.9 = 6.96757233 x = 6.96757233 Simplifying x = 6.96757233Subproblem 2
x + -3.9 = -3.06757233 Simplifying x + -3.9 = -3.06757233 Reorder the terms: -3.9 + x = -3.06757233 Solving -3.9 + x = -3.06757233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = -3.06757233 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -3.06757233 + 3.9 x = -3.06757233 + 3.9 Combine like terms: -3.06757233 + 3.9 = 0.83242767 x = 0.83242767 Simplifying x = 0.83242767Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.96757233, 0.83242767}
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