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Simplifying 5x2 + -26x + 33.8 = 0 Reorder the terms: 33.8 + -26x + 5x2 = 0 Solving 33.8 + -26x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.76 + -5.2x + x2 = 0 Move the constant term to the right: Add '-6.76' to each side of the equation. 6.76 + -5.2x + -6.76 + x2 = 0 + -6.76 Reorder the terms: 6.76 + -6.76 + -5.2x + x2 = 0 + -6.76 Combine like terms: 6.76 + -6.76 = 0.00 0.00 + -5.2x + x2 = 0 + -6.76 -5.2x + x2 = 0 + -6.76 Combine like terms: 0 + -6.76 = -6.76 -5.2x + x2 = -6.76 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -6.76 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -6.76 + 6.76 Combine like terms: -6.76 + 6.76 = 0.00 6.76 + -5.2x + x2 = 0.00 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -2.6) equal to 0.00 and 0.00.Subproblem 1
x + -2.6 = 0.00 Simplifying x + -2.6 = 0.00 Reorder the terms: -2.6 + x = 0.00 Solving -2.6 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 0.00 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 0.00 + 2.6 x = 0.00 + 2.6 Combine like terms: 0.00 + 2.6 = 2.6 x = 2.6 Simplifying x = 2.6Subproblem 2
x + -2.6 = 0.00 Simplifying x + -2.6 = 0.00 Reorder the terms: -2.6 + x = 0.00 Solving -2.6 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 0.00 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 0.00 + 2.6 x = 0.00 + 2.6 Combine like terms: 0.00 + 2.6 = 2.6 x = 2.6 Simplifying x = 2.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6, 2.6}
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