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Simplifying 5x2 + -23x + -50 = 0 Reorder the terms: -50 + -23x + 5x2 = 0 Solving -50 + -23x + 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'. -10 + -4.6x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4.6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4.6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4.6x + x2 = 0 + 10 -4.6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4.6x + x2 = 10 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 10 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 10 + 5.29 Combine like terms: 10 + 5.29 = 15.29 5.29 + -4.6x + x2 = 15.29 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 15.29 Calculate the square root of the right side: 3.910242959 Break this problem into two subproblems by setting (x + -2.3) equal to 3.910242959 and -3.910242959.Subproblem 1
x + -2.3 = 3.910242959 Simplifying x + -2.3 = 3.910242959 Reorder the terms: -2.3 + x = 3.910242959 Solving -2.3 + x = 3.910242959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 3.910242959 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 3.910242959 + 2.3 x = 3.910242959 + 2.3 Combine like terms: 3.910242959 + 2.3 = 6.210242959 x = 6.210242959 Simplifying x = 6.210242959Subproblem 2
x + -2.3 = -3.910242959 Simplifying x + -2.3 = -3.910242959 Reorder the terms: -2.3 + x = -3.910242959 Solving -2.3 + x = -3.910242959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -3.910242959 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -3.910242959 + 2.3 x = -3.910242959 + 2.3 Combine like terms: -3.910242959 + 2.3 = -1.610242959 x = -1.610242959 Simplifying x = -1.610242959Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.210242959, -1.610242959}
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