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Simplifying 5x2 + -33x + 21 = 0 Reorder the terms: 21 + -33x + 5x2 = 0 Solving 21 + -33x + 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'. 4.2 + -6.6x + x2 = 0 Move the constant term to the right: Add '-4.2' to each side of the equation. 4.2 + -6.6x + -4.2 + x2 = 0 + -4.2 Reorder the terms: 4.2 + -4.2 + -6.6x + x2 = 0 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + -6.6x + x2 = 0 + -4.2 -6.6x + x2 = 0 + -4.2 Combine like terms: 0 + -4.2 = -4.2 -6.6x + x2 = -4.2 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -4.2 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -4.2 + 10.89 Combine like terms: -4.2 + 10.89 = 6.69 10.89 + -6.6x + x2 = 6.69 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 6.69 Calculate the square root of the right side: 2.586503431 Break this problem into two subproblems by setting (x + -3.3) equal to 2.586503431 and -2.586503431.Subproblem 1
x + -3.3 = 2.586503431 Simplifying x + -3.3 = 2.586503431 Reorder the terms: -3.3 + x = 2.586503431 Solving -3.3 + x = 2.586503431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 2.586503431 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 2.586503431 + 3.3 x = 2.586503431 + 3.3 Combine like terms: 2.586503431 + 3.3 = 5.886503431 x = 5.886503431 Simplifying x = 5.886503431Subproblem 2
x + -3.3 = -2.586503431 Simplifying x + -3.3 = -2.586503431 Reorder the terms: -3.3 + x = -2.586503431 Solving -3.3 + x = -2.586503431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -2.586503431 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -2.586503431 + 3.3 x = -2.586503431 + 3.3 Combine like terms: -2.586503431 + 3.3 = 0.713496569 x = 0.713496569 Simplifying x = 0.713496569Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.886503431, 0.713496569}
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