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Simplifying 13 + 3x + -5x2 = 0 Solving 13 + 3x + -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'. -2.6 + -0.6x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -0.6x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -0.6x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -0.6x + x2 = 0 + 2.6 -0.6x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -0.6x + x2 = 2.6 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 2.6 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 2.6 + 0.09 Combine like terms: 2.6 + 0.09 = 2.69 0.09 + -0.6x + x2 = 2.69 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (x + -0.3) equal to 1.640121947 and -1.640121947.Subproblem 1
x + -0.3 = 1.640121947 Simplifying x + -0.3 = 1.640121947 Reorder the terms: -0.3 + x = 1.640121947 Solving -0.3 + x = 1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.640121947 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.640121947 + 0.3 x = 1.640121947 + 0.3 Combine like terms: 1.640121947 + 0.3 = 1.940121947 x = 1.940121947 Simplifying x = 1.940121947Subproblem 2
x + -0.3 = -1.640121947 Simplifying x + -0.3 = -1.640121947 Reorder the terms: -0.3 + x = -1.640121947 Solving -0.3 + x = -1.640121947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.640121947 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.640121947 + 0.3 x = -1.640121947 + 0.3 Combine like terms: -1.640121947 + 0.3 = -1.340121947 x = -1.340121947 Simplifying x = -1.340121947Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.940121947, -1.340121947}
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