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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 + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + -1x2 = 0 Solving 5 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 12x + x2 = 0 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 = 41 36 + 12x + x2 = 41 Factor a perfect square on the left side: (x + 6)(x + 6) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 6) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 6 = 6.403124237 Simplifying x + 6 = 6.403124237 Reorder the terms: 6 + x = 6.403124237 Solving 6 + x = 6.403124237 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 = 6.403124237 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.403124237 + -6 x = 6.403124237 + -6 Combine like terms: 6.403124237 + -6 = 0.403124237 x = 0.403124237 Simplifying x = 0.403124237Subproblem 2
x + 6 = -6.403124237 Simplifying x + 6 = -6.403124237 Reorder the terms: 6 + x = -6.403124237 Solving 6 + x = -6.403124237 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 = -6.403124237 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.403124237 + -6 x = -6.403124237 + -6 Combine like terms: -6.403124237 + -6 = -12.403124237 x = -12.403124237 Simplifying x = -12.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.403124237, -12.403124237}Solution
x = {0.403124237, -12.403124237}
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