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Simplifying 5x2 + -39x + -28 = 0 Reorder the terms: -28 + -39x + 5x2 = 0 Solving -28 + -39x + 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'. -5.6 + -7.8x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -7.8x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -7.8x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -7.8x + x2 = 0 + 5.6 -7.8x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -7.8x + x2 = 5.6 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 = 5.6 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = 5.6 + 15.21 Combine like terms: 5.6 + 15.21 = 20.81 15.21 + -7.8x + x2 = 20.81 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 20.81 Calculate the square root of the right side: 4.561797891 Break this problem into two subproblems by setting (x + -3.9) equal to 4.561797891 and -4.561797891.Subproblem 1
x + -3.9 = 4.561797891 Simplifying x + -3.9 = 4.561797891 Reorder the terms: -3.9 + x = 4.561797891 Solving -3.9 + x = 4.561797891 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 = 4.561797891 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 4.561797891 + 3.9 x = 4.561797891 + 3.9 Combine like terms: 4.561797891 + 3.9 = 8.461797891 x = 8.461797891 Simplifying x = 8.461797891Subproblem 2
x + -3.9 = -4.561797891 Simplifying x + -3.9 = -4.561797891 Reorder the terms: -3.9 + x = -4.561797891 Solving -3.9 + x = -4.561797891 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 = -4.561797891 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -4.561797891 + 3.9 x = -4.561797891 + 3.9 Combine like terms: -4.561797891 + 3.9 = -0.661797891 x = -0.661797891 Simplifying x = -0.661797891Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.461797891, -0.661797891}
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