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Simplifying 5x2 + -33x + -15 = 0 Reorder the terms: -15 + -33x + 5x2 = 0 Solving -15 + -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'. -3 + -6.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6.6x + x2 = 0 + 3 -6.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6.6x + x2 = 3 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 = 3 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = 3 + 10.89 Combine like terms: 3 + 10.89 = 13.89 10.89 + -6.6x + x2 = 13.89 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 13.89 Calculate the square root of the right side: 3.726929031 Break this problem into two subproblems by setting (x + -3.3) equal to 3.726929031 and -3.726929031.Subproblem 1
x + -3.3 = 3.726929031 Simplifying x + -3.3 = 3.726929031 Reorder the terms: -3.3 + x = 3.726929031 Solving -3.3 + x = 3.726929031 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 = 3.726929031 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 3.726929031 + 3.3 x = 3.726929031 + 3.3 Combine like terms: 3.726929031 + 3.3 = 7.026929031 x = 7.026929031 Simplifying x = 7.026929031Subproblem 2
x + -3.3 = -3.726929031 Simplifying x + -3.3 = -3.726929031 Reorder the terms: -3.3 + x = -3.726929031 Solving -3.3 + x = -3.726929031 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 = -3.726929031 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -3.726929031 + 3.3 x = -3.726929031 + 3.3 Combine like terms: -3.726929031 + 3.3 = -0.426929031 x = -0.426929031 Simplifying x = -0.426929031Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.026929031, -0.426929031}
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