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Simplifying 5x2 + -13x + -10 = 0 Reorder the terms: -10 + -13x + 5x2 = 0 Solving -10 + -13x + 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'. -2 + -2.6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.6x + x2 = 0 + 2 -2.6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.6x + x2 = 2 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = 2 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = 2 + 1.69 Combine like terms: 2 + 1.69 = 3.69 1.69 + -2.6x + x2 = 3.69 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 3.69 Calculate the square root of the right side: 1.920937271 Break this problem into two subproblems by setting (x + -1.3) equal to 1.920937271 and -1.920937271.Subproblem 1
x + -1.3 = 1.920937271 Simplifying x + -1.3 = 1.920937271 Reorder the terms: -1.3 + x = 1.920937271 Solving -1.3 + x = 1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 1.920937271 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 1.920937271 + 1.3 x = 1.920937271 + 1.3 Combine like terms: 1.920937271 + 1.3 = 3.220937271 x = 3.220937271 Simplifying x = 3.220937271Subproblem 2
x + -1.3 = -1.920937271 Simplifying x + -1.3 = -1.920937271 Reorder the terms: -1.3 + x = -1.920937271 Solving -1.3 + x = -1.920937271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -1.920937271 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -1.920937271 + 1.3 x = -1.920937271 + 1.3 Combine like terms: -1.920937271 + 1.3 = -0.620937271 x = -0.620937271 Simplifying x = -0.620937271Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.220937271, -0.620937271}
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