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Simplifying 5x2 + 33x + -32 = 0 Reorder the terms: -32 + 33x + 5x2 = 0 Solving -32 + 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'. -6.4 + 6.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 6.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 6.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 6.6x + x2 = 0 + 6.4 6.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 6.6x + x2 = 6.4 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 = 6.4 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = 6.4 + 10.89 Combine like terms: 6.4 + 10.89 = 17.29 10.89 + 6.6x + x2 = 17.29 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 17.29 Calculate the square root of the right side: 4.158124577 Break this problem into two subproblems by setting (x + 3.3) equal to 4.158124577 and -4.158124577.Subproblem 1
x + 3.3 = 4.158124577 Simplifying x + 3.3 = 4.158124577 Reorder the terms: 3.3 + x = 4.158124577 Solving 3.3 + x = 4.158124577 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 = 4.158124577 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 4.158124577 + -3.3 x = 4.158124577 + -3.3 Combine like terms: 4.158124577 + -3.3 = 0.858124577 x = 0.858124577 Simplifying x = 0.858124577Subproblem 2
x + 3.3 = -4.158124577 Simplifying x + 3.3 = -4.158124577 Reorder the terms: 3.3 + x = -4.158124577 Solving 3.3 + x = -4.158124577 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 = -4.158124577 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -4.158124577 + -3.3 x = -4.158124577 + -3.3 Combine like terms: -4.158124577 + -3.3 = -7.458124577 x = -7.458124577 Simplifying x = -7.458124577Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.858124577, -7.458124577}
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