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Simplifying 2x(x + -5) = 19 Reorder the terms: 2x(-5 + x) = 19 (-5 * 2x + x * 2x) = 19 (-10x + 2x2) = 19 Solving -10x + 2x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -10x + 2x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -5x + x2 = 0 + 9.5 -5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -5x + x2 = 9.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 9.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 9.5 + 6.25 Combine like terms: 9.5 + 6.25 = 15.75 6.25 + -5x + x2 = 15.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + -2.5) equal to 3.968626967 and -3.968626967.Subproblem 1
x + -2.5 = 3.968626967 Simplifying x + -2.5 = 3.968626967 Reorder the terms: -2.5 + x = 3.968626967 Solving -2.5 + x = 3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.968626967 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.968626967 + 2.5 x = 3.968626967 + 2.5 Combine like terms: 3.968626967 + 2.5 = 6.468626967 x = 6.468626967 Simplifying x = 6.468626967Subproblem 2
x + -2.5 = -3.968626967 Simplifying x + -2.5 = -3.968626967 Reorder the terms: -2.5 + x = -3.968626967 Solving -2.5 + x = -3.968626967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.968626967 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.968626967 + 2.5 x = -3.968626967 + 2.5 Combine like terms: -3.968626967 + 2.5 = -1.468626967 x = -1.468626967 Simplifying x = -1.468626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.468626967, -1.468626967}
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