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Simplifying -5x2 + -9x + 39 = 0 Reorder the terms: 39 + -9x + -5x2 = 0 Solving 39 + -9x + -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'. -7.8 + 1.8x + x2 = 0 Move the constant term to the right: Add '7.8' to each side of the equation. -7.8 + 1.8x + 7.8 + x2 = 0 + 7.8 Reorder the terms: -7.8 + 7.8 + 1.8x + x2 = 0 + 7.8 Combine like terms: -7.8 + 7.8 = 0.0 0.0 + 1.8x + x2 = 0 + 7.8 1.8x + x2 = 0 + 7.8 Combine like terms: 0 + 7.8 = 7.8 1.8x + x2 = 7.8 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 7.8 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 7.8 + 0.81 Combine like terms: 7.8 + 0.81 = 8.61 0.81 + 1.8x + x2 = 8.61 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 8.61 Calculate the square root of the right side: 2.93428015 Break this problem into two subproblems by setting (x + 0.9) equal to 2.93428015 and -2.93428015.Subproblem 1
x + 0.9 = 2.93428015 Simplifying x + 0.9 = 2.93428015 Reorder the terms: 0.9 + x = 2.93428015 Solving 0.9 + x = 2.93428015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.93428015 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.93428015 + -0.9 x = 2.93428015 + -0.9 Combine like terms: 2.93428015 + -0.9 = 2.03428015 x = 2.03428015 Simplifying x = 2.03428015Subproblem 2
x + 0.9 = -2.93428015 Simplifying x + 0.9 = -2.93428015 Reorder the terms: 0.9 + x = -2.93428015 Solving 0.9 + x = -2.93428015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.93428015 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.93428015 + -0.9 x = -2.93428015 + -0.9 Combine like terms: -2.93428015 + -0.9 = -3.83428015 x = -3.83428015 Simplifying x = -3.83428015Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.03428015, -3.83428015}
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