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Simplifying 2x2 + 24x + -29 = 0 Reorder the terms: -29 + 24x + 2x2 = 0 Solving -29 + 24x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + 12x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 12x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 12x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 12x + x2 = 0 + 14.5 12x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 12x + x2 = 14.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 14.5 + 36 Reorder the terms: 36 + 12x + x2 = 14.5 + 36 Combine like terms: 14.5 + 36 = 50.5 36 + 12x + x2 = 50.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 50.5 Calculate the square root of the right side: 7.106335202 Break this problem into two subproblems by setting (x + 6) equal to 7.106335202 and -7.106335202.Subproblem 1
x + 6 = 7.106335202 Simplifying x + 6 = 7.106335202 Reorder the terms: 6 + x = 7.106335202 Solving 6 + x = 7.106335202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.106335202 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.106335202 + -6 x = 7.106335202 + -6 Combine like terms: 7.106335202 + -6 = 1.106335202 x = 1.106335202 Simplifying x = 1.106335202Subproblem 2
x + 6 = -7.106335202 Simplifying x + 6 = -7.106335202 Reorder the terms: 6 + x = -7.106335202 Solving 6 + x = -7.106335202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.106335202 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.106335202 + -6 x = -7.106335202 + -6 Combine like terms: -7.106335202 + -6 = -13.106335202 x = -13.106335202 Simplifying x = -13.106335202Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.106335202, -13.106335202}
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