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Simplifying 5x2 + -39x + 20 = 0 Reorder the terms: 20 + -39x + 5x2 = 0 Solving 20 + -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'. 4 + -7.8x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7.8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.8x + x2 = 0 + -4 -7.8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.8x + x2 = -4 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 = -4 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = -4 + 15.21 Combine like terms: -4 + 15.21 = 11.21 15.21 + -7.8x + x2 = 11.21 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 11.21 Calculate the square root of the right side: 3.348133809 Break this problem into two subproblems by setting (x + -3.9) equal to 3.348133809 and -3.348133809.Subproblem 1
x + -3.9 = 3.348133809 Simplifying x + -3.9 = 3.348133809 Reorder the terms: -3.9 + x = 3.348133809 Solving -3.9 + x = 3.348133809 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 = 3.348133809 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 3.348133809 + 3.9 x = 3.348133809 + 3.9 Combine like terms: 3.348133809 + 3.9 = 7.248133809 x = 7.248133809 Simplifying x = 7.248133809Subproblem 2
x + -3.9 = -3.348133809 Simplifying x + -3.9 = -3.348133809 Reorder the terms: -3.9 + x = -3.348133809 Solving -3.9 + x = -3.348133809 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 = -3.348133809 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -3.348133809 + 3.9 x = -3.348133809 + 3.9 Combine like terms: -3.348133809 + 3.9 = 0.551866191 x = 0.551866191 Simplifying x = 0.551866191Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.248133809, 0.551866191}
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