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Simplifying 5x2 + 4x + 5 = 43x Reorder the terms: 5 + 4x + 5x2 = 43x Solving 5 + 4x + 5x2 = 43x Solving for variable 'x'. Reorder the terms: 5 + 4x + -43x + 5x2 = 43x + -43x Combine like terms: 4x + -43x = -39x 5 + -39x + 5x2 = 43x + -43x Combine like terms: 43x + -43x = 0 5 + -39x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -7.8x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -7.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7.8x + x2 = 0 + -1 -7.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -7.8x + x2 = -1 The x term is -7.8x. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8x + 15.21 + x2 = -1 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = -1 + 15.21 Combine like terms: -1 + 15.21 = 14.21 15.21 + -7.8x + x2 = 14.21 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 14.21 Calculate the square root of the right side: 3.769615365 Break this problem into two subproblems by setting (x + -3.9) equal to 3.769615365 and -3.769615365.Subproblem 1
x + -3.9 = 3.769615365 Simplifying x + -3.9 = 3.769615365 Reorder the terms: -3.9 + x = 3.769615365 Solving -3.9 + x = 3.769615365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = 3.769615365 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 3.769615365 + 3.9 x = 3.769615365 + 3.9 Combine like terms: 3.769615365 + 3.9 = 7.669615365 x = 7.669615365 Simplifying x = 7.669615365Subproblem 2
x + -3.9 = -3.769615365 Simplifying x + -3.9 = -3.769615365 Reorder the terms: -3.9 + x = -3.769615365 Solving -3.9 + x = -3.769615365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = -3.769615365 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -3.769615365 + 3.9 x = -3.769615365 + 3.9 Combine like terms: -3.769615365 + 3.9 = 0.130384635 x = 0.130384635 Simplifying x = 0.130384635Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.669615365, 0.130384635}
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