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Simplifying 2(x) = 2x2 + -20x + 7 Reorder the terms: 2x = 7 + -20x + 2x2 Solving 2x = 7 + -20x + 2x2 Solving for variable 'x'. Reorder the terms: -7 + 2x + 20x + -2x2 = 7 + -20x + 2x2 + -7 + 20x + -2x2 Combine like terms: 2x + 20x = 22x -7 + 22x + -2x2 = 7 + -20x + 2x2 + -7 + 20x + -2x2 Reorder the terms: -7 + 22x + -2x2 = 7 + -7 + -20x + 20x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -7 + 22x + -2x2 = 0 + -20x + 20x + 2x2 + -2x2 -7 + 22x + -2x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 -7 + 22x + -2x2 = 0 + 2x2 + -2x2 -7 + 22x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -7 + 22x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -11x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -11x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -11x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -11x + x2 = 0 + -3.5 -11x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -11x + x2 = -3.5 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -3.5 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -3.5 + 30.25 Combine like terms: -3.5 + 30.25 = 26.75 30.25 + -11x + x2 = 26.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 26.75 Calculate the square root of the right side: 5.172040216 Break this problem into two subproblems by setting (x + -5.5) equal to 5.172040216 and -5.172040216.Subproblem 1
x + -5.5 = 5.172040216 Simplifying x + -5.5 = 5.172040216 Reorder the terms: -5.5 + x = 5.172040216 Solving -5.5 + x = 5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.172040216 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.172040216 + 5.5 x = 5.172040216 + 5.5 Combine like terms: 5.172040216 + 5.5 = 10.672040216 x = 10.672040216 Simplifying x = 10.672040216Subproblem 2
x + -5.5 = -5.172040216 Simplifying x + -5.5 = -5.172040216 Reorder the terms: -5.5 + x = -5.172040216 Solving -5.5 + x = -5.172040216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.172040216 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.172040216 + 5.5 x = -5.172040216 + 5.5 Combine like terms: -5.172040216 + 5.5 = 0.327959784 x = 0.327959784 Simplifying x = 0.327959784Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.672040216, 0.327959784}
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