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Simplifying 2x2 + -24x + -3 = 0 Reorder the terms: -3 + -24x + 2x2 = 0 Solving -3 + -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'. -1.5 + -12x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -12x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -12x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -12x + x2 = 0 + 1.5 -12x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -12x + x2 = 1.5 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 = 1.5 + 36 Reorder the terms: 36 + -12x + x2 = 1.5 + 36 Combine like terms: 1.5 + 36 = 37.5 36 + -12x + x2 = 37.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 37.5 Calculate the square root of the right side: 6.123724357 Break this problem into two subproblems by setting (x + -6) equal to 6.123724357 and -6.123724357.Subproblem 1
x + -6 = 6.123724357 Simplifying x + -6 = 6.123724357 Reorder the terms: -6 + x = 6.123724357 Solving -6 + x = 6.123724357 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 = 6.123724357 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.123724357 + 6 x = 6.123724357 + 6 Combine like terms: 6.123724357 + 6 = 12.123724357 x = 12.123724357 Simplifying x = 12.123724357Subproblem 2
x + -6 = -6.123724357 Simplifying x + -6 = -6.123724357 Reorder the terms: -6 + x = -6.123724357 Solving -6 + x = -6.123724357 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 = -6.123724357 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.123724357 + 6 x = -6.123724357 + 6 Combine like terms: -6.123724357 + 6 = -0.123724357 x = -0.123724357 Simplifying x = -0.123724357Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.123724357, -0.123724357}
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