5x^2+11x-8=0 - Solution

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5x^2+11x-8=0

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Solution for 5x^2+11x-8=0 equation:

Simplifying 5x2 + 11x + -8 = 0 Reorder the terms: -8 + 11x + 5x2 = 0 Solving -8 + 11x + 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'. -1.6 + 2.2x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 2.2x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 2.2x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 2.2x + x2 = 0 + 1.6 2.2x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 2.2x + x2 = 1.6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 1.6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 1.6 + 1.21 Combine like terms: 1.6 + 1.21 = 2.81 1.21 + 2.2x + x2 = 2.81 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (x + 1.1) equal to 1.676305461 and -1.676305461.

Subproblem 1

x + 1.1 = 1.676305461 Simplifying x + 1.1 = 1.676305461 Reorder the terms: 1.1 + x = 1.676305461 Solving 1.1 + x = 1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.676305461 + -1.1 x = 1.676305461 + -1.1 Combine like terms: 1.676305461 + -1.1 = 0.576305461 x = 0.576305461 Simplifying x = 0.576305461

Subproblem 2

x + 1.1 = -1.676305461 Simplifying x + 1.1 = -1.676305461 Reorder the terms: 1.1 + x = -1.676305461 Solving 1.1 + x = -1.676305461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.676305461 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.676305461 + -1.1 x = -1.676305461 + -1.1 Combine like terms: -1.676305461 + -1.1 = -2.776305461 x = -2.776305461 Simplifying x = -2.776305461

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.576305461, -2.776305461}

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