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Simplifying 5x2 + -28x + 34 = 0 Reorder the terms: 34 + -28x + 5x2 = 0 Solving 34 + -28x + 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'. 6.8 + -5.6x + x2 = 0 Move the constant term to the right: Add '-6.8' to each side of the equation. 6.8 + -5.6x + -6.8 + x2 = 0 + -6.8 Reorder the terms: 6.8 + -6.8 + -5.6x + x2 = 0 + -6.8 Combine like terms: 6.8 + -6.8 = 0.0 0.0 + -5.6x + x2 = 0 + -6.8 -5.6x + x2 = 0 + -6.8 Combine like terms: 0 + -6.8 = -6.8 -5.6x + x2 = -6.8 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = -6.8 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = -6.8 + 7.84 Combine like terms: -6.8 + 7.84 = 1.04 7.84 + -5.6x + x2 = 1.04 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + -2.8) equal to 1.019803903 and -1.019803903.Subproblem 1
x + -2.8 = 1.019803903 Simplifying x + -2.8 = 1.019803903 Reorder the terms: -2.8 + x = 1.019803903 Solving -2.8 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 1.019803903 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 1.019803903 + 2.8 x = 1.019803903 + 2.8 Combine like terms: 1.019803903 + 2.8 = 3.819803903 x = 3.819803903 Simplifying x = 3.819803903Subproblem 2
x + -2.8 = -1.019803903 Simplifying x + -2.8 = -1.019803903 Reorder the terms: -2.8 + x = -1.019803903 Solving -2.8 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -1.019803903 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -1.019803903 + 2.8 x = -1.019803903 + 2.8 Combine like terms: -1.019803903 + 2.8 = 1.780196097 x = 1.780196097 Simplifying x = 1.780196097Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.819803903, 1.780196097}
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