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Simplifying 2x2 + -24x = -7 Reorder the terms: -24x + 2x2 = -7 Solving -24x + 2x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + -24x + 2x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -12x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -12x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -12x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -12x + x2 = 0 + -3.5 -12x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -12x + x2 = -3.5 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 = -3.5 + 36 Reorder the terms: 36 + -12x + x2 = -3.5 + 36 Combine like terms: -3.5 + 36 = 32.5 36 + -12x + x2 = 32.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (x + -6) equal to 5.700877125 and -5.700877125.Subproblem 1
x + -6 = 5.700877125 Simplifying x + -6 = 5.700877125 Reorder the terms: -6 + x = 5.700877125 Solving -6 + x = 5.700877125 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 = 5.700877125 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.700877125 + 6 x = 5.700877125 + 6 Combine like terms: 5.700877125 + 6 = 11.700877125 x = 11.700877125 Simplifying x = 11.700877125Subproblem 2
x + -6 = -5.700877125 Simplifying x + -6 = -5.700877125 Reorder the terms: -6 + x = -5.700877125 Solving -6 + x = -5.700877125 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 = -5.700877125 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.700877125 + 6 x = -5.700877125 + 6 Combine like terms: -5.700877125 + 6 = 0.299122875 x = 0.299122875 Simplifying x = 0.299122875Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.700877125, 0.299122875}
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