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Simplifying -2x2 + -24x + -51 = 0 Reorder the terms: -51 + -24x + -2x2 = 0 Solving -51 + -24x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(51 + 24x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(51 + 24x + 2x2)' equal to zero and attempt to solve: Simplifying 51 + 24x + 2x2 = 0 Solving 51 + 24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + 12x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + 12x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + 12x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + 12x + x2 = 0 + -25.5 12x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 12x + x2 = -25.5 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 = -25.5 + 36 Reorder the terms: 36 + 12x + x2 = -25.5 + 36 Combine like terms: -25.5 + 36 = 10.5 36 + 12x + x2 = 10.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + 6) equal to 3.240370349 and -3.240370349.Subproblem 1
x + 6 = 3.240370349 Simplifying x + 6 = 3.240370349 Reorder the terms: 6 + x = 3.240370349 Solving 6 + x = 3.240370349 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 = 3.240370349 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.240370349 + -6 x = 3.240370349 + -6 Combine like terms: 3.240370349 + -6 = -2.759629651 x = -2.759629651 Simplifying x = -2.759629651Subproblem 2
x + 6 = -3.240370349 Simplifying x + 6 = -3.240370349 Reorder the terms: 6 + x = -3.240370349 Solving 6 + x = -3.240370349 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 = -3.240370349 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.240370349 + -6 x = -3.240370349 + -6 Combine like terms: -3.240370349 + -6 = -9.240370349 x = -9.240370349 Simplifying x = -9.240370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.759629651, -9.240370349}Solution
x = {-2.759629651, -9.240370349}
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