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Simplifying -5x(x + 2) + -3x = -50 Reorder the terms: -5x(2 + x) + -3x = -50 (2 * -5x + x * -5x) + -3x = -50 (-10x + -5x2) + -3x = -50 Reorder the terms: -10x + -3x + -5x2 = -50 Combine like terms: -10x + -3x = -13x -13x + -5x2 = -50 Solving -13x + -5x2 = -50 Solving for variable 'x'. Reorder the terms: 50 + -13x + -5x2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10 + 2.6x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2.6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.6x + x2 = 0 + 10 2.6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.6x + x2 = 10 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 = 10 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 10 + 1.69 Combine like terms: 10 + 1.69 = 11.69 1.69 + 2.6x + x2 = 11.69 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 11.69 Calculate the square root of the right side: 3.419064199 Break this problem into two subproblems by setting (x + 1.3) equal to 3.419064199 and -3.419064199.Subproblem 1
x + 1.3 = 3.419064199 Simplifying x + 1.3 = 3.419064199 Reorder the terms: 1.3 + x = 3.419064199 Solving 1.3 + x = 3.419064199 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 = 3.419064199 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 3.419064199 + -1.3 x = 3.419064199 + -1.3 Combine like terms: 3.419064199 + -1.3 = 2.119064199 x = 2.119064199 Simplifying x = 2.119064199Subproblem 2
x + 1.3 = -3.419064199 Simplifying x + 1.3 = -3.419064199 Reorder the terms: 1.3 + x = -3.419064199 Solving 1.3 + x = -3.419064199 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 = -3.419064199 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -3.419064199 + -1.3 x = -3.419064199 + -1.3 Combine like terms: -3.419064199 + -1.3 = -4.719064199 x = -4.719064199 Simplifying x = -4.719064199Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.119064199, -4.719064199}
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