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Simplifying 216 = 4x2 + 22x Reorder the terms: 216 = 22x + 4x2 Solving 216 = 22x + 4x2 Solving for variable 'x'. Reorder the terms: 216 + -22x + -4x2 = 22x + -22x + 4x2 + -4x2 Combine like terms: 22x + -22x = 0 216 + -22x + -4x2 = 0 + 4x2 + -4x2 216 + -22x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 216 + -22x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(108 + -11x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(108 + -11x + -2x2)' equal to zero and attempt to solve: Simplifying 108 + -11x + -2x2 = 0 Solving 108 + -11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -54 + 5.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + 5.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 5.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 5.5x + x2 = 0 + 54 5.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 5.5x + x2 = 54 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 54 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 54 + 7.5625 Combine like terms: 54 + 7.5625 = 61.5625 7.5625 + 5.5x + x2 = 61.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 61.5625 Calculate the square root of the right side: 7.846177413 Break this problem into two subproblems by setting (x + 2.75) equal to 7.846177413 and -7.846177413.Subproblem 1
x + 2.75 = 7.846177413 Simplifying x + 2.75 = 7.846177413 Reorder the terms: 2.75 + x = 7.846177413 Solving 2.75 + x = 7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 7.846177413 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 7.846177413 + -2.75 x = 7.846177413 + -2.75 Combine like terms: 7.846177413 + -2.75 = 5.096177413 x = 5.096177413 Simplifying x = 5.096177413Subproblem 2
x + 2.75 = -7.846177413 Simplifying x + 2.75 = -7.846177413 Reorder the terms: 2.75 + x = -7.846177413 Solving 2.75 + x = -7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -7.846177413 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -7.846177413 + -2.75 x = -7.846177413 + -2.75 Combine like terms: -7.846177413 + -2.75 = -10.596177413 x = -10.596177413 Simplifying x = -10.596177413Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.096177413, -10.596177413}Solution
x = {5.096177413, -10.596177413}
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