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Simplifying 5x2 + -73x + 30 = 0 Reorder the terms: 30 + -73x + 5x2 = 0 Solving 30 + -73x + 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'. 6 + -14.6x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -14.6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -14.6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -14.6x + x2 = 0 + -6 -14.6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -14.6x + x2 = -6 The x term is -14.6x. Take half its coefficient (-7.3). Square it (53.29) and add it to both sides. Add '53.29' to each side of the equation. -14.6x + 53.29 + x2 = -6 + 53.29 Reorder the terms: 53.29 + -14.6x + x2 = -6 + 53.29 Combine like terms: -6 + 53.29 = 47.29 53.29 + -14.6x + x2 = 47.29 Factor a perfect square on the left side: (x + -7.3)(x + -7.3) = 47.29 Calculate the square root of the right side: 6.876772499 Break this problem into two subproblems by setting (x + -7.3) equal to 6.876772499 and -6.876772499.Subproblem 1
x + -7.3 = 6.876772499 Simplifying x + -7.3 = 6.876772499 Reorder the terms: -7.3 + x = 6.876772499 Solving -7.3 + x = 6.876772499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.3' to each side of the equation. -7.3 + 7.3 + x = 6.876772499 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + x = 6.876772499 + 7.3 x = 6.876772499 + 7.3 Combine like terms: 6.876772499 + 7.3 = 14.176772499 x = 14.176772499 Simplifying x = 14.176772499Subproblem 2
x + -7.3 = -6.876772499 Simplifying x + -7.3 = -6.876772499 Reorder the terms: -7.3 + x = -6.876772499 Solving -7.3 + x = -6.876772499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.3' to each side of the equation. -7.3 + 7.3 + x = -6.876772499 + 7.3 Combine like terms: -7.3 + 7.3 = 0.0 0.0 + x = -6.876772499 + 7.3 x = -6.876772499 + 7.3 Combine like terms: -6.876772499 + 7.3 = 0.423227501 x = 0.423227501 Simplifying x = 0.423227501Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.176772499, 0.423227501}
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