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Simplifying 2x2 + 24x = -10 Reorder the terms: 24x + 2x2 = -10 Solving 24x + 2x2 = -10 Solving for variable 'x'. Reorder the terms: 10 + 24x + 2x2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + 24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 12x + x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + x2 = 0 Solving 5 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 12x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 12x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 12x + x2 = 0 + -5 12x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 12x + x2 = -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 = -5 + 36 Reorder the terms: 36 + 12x + x2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + 12x + x2 = 31 Factor a perfect square on the left side: (x + 6)(x + 6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 6) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 6 = 5.567764363 Simplifying x + 6 = 5.567764363 Reorder the terms: 6 + x = 5.567764363 Solving 6 + x = 5.567764363 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 = 5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.567764363 + -6 x = 5.567764363 + -6 Combine like terms: 5.567764363 + -6 = -0.432235637 x = -0.432235637 Simplifying x = -0.432235637Subproblem 2
x + 6 = -5.567764363 Simplifying x + 6 = -5.567764363 Reorder the terms: 6 + x = -5.567764363 Solving 6 + x = -5.567764363 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 = -5.567764363 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.567764363 + -6 x = -5.567764363 + -6 Combine like terms: -5.567764363 + -6 = -11.567764363 x = -11.567764363 Simplifying x = -11.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.432235637, -11.567764363}Solution
x = {-0.432235637, -11.567764363}
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