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Simplifying 5x2 + -26x + -25 = 0 Reorder the terms: -25 + -26x + 5x2 = 0 Solving -25 + -26x + 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 + -5.2x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -5.2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.2x + x2 = 0 + 5 -5.2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.2x + x2 = 5 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 5 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 5 + 6.76 Combine like terms: 5 + 6.76 = 11.76 6.76 + -5.2x + x2 = 11.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 11.76 Calculate the square root of the right side: 3.42928564 Break this problem into two subproblems by setting (x + -2.6) equal to 3.42928564 and -3.42928564.Subproblem 1
x + -2.6 = 3.42928564 Simplifying x + -2.6 = 3.42928564 Reorder the terms: -2.6 + x = 3.42928564 Solving -2.6 + x = 3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 3.42928564 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 3.42928564 + 2.6 x = 3.42928564 + 2.6 Combine like terms: 3.42928564 + 2.6 = 6.02928564 x = 6.02928564 Simplifying x = 6.02928564Subproblem 2
x + -2.6 = -3.42928564 Simplifying x + -2.6 = -3.42928564 Reorder the terms: -2.6 + x = -3.42928564 Solving -2.6 + x = -3.42928564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -3.42928564 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -3.42928564 + 2.6 x = -3.42928564 + 2.6 Combine like terms: -3.42928564 + 2.6 = -0.82928564 x = -0.82928564 Simplifying x = -0.82928564Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.02928564, -0.82928564}
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