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Simplifying 5x2 + 50x + -156 = 0 Reorder the terms: -156 + 50x + 5x2 = 0 Solving -156 + 50x + 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'. -31.2 + 10x + x2 = 0 Move the constant term to the right: Add '31.2' to each side of the equation. -31.2 + 10x + 31.2 + x2 = 0 + 31.2 Reorder the terms: -31.2 + 31.2 + 10x + x2 = 0 + 31.2 Combine like terms: -31.2 + 31.2 = 0.0 0.0 + 10x + x2 = 0 + 31.2 10x + x2 = 0 + 31.2 Combine like terms: 0 + 31.2 = 31.2 10x + x2 = 31.2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 31.2 + 25 Reorder the terms: 25 + 10x + x2 = 31.2 + 25 Combine like terms: 31.2 + 25 = 56.2 25 + 10x + x2 = 56.2 Factor a perfect square on the left side: (x + 5)(x + 5) = 56.2 Calculate the square root of the right side: 7.496665926 Break this problem into two subproblems by setting (x + 5) equal to 7.496665926 and -7.496665926.Subproblem 1
x + 5 = 7.496665926 Simplifying x + 5 = 7.496665926 Reorder the terms: 5 + x = 7.496665926 Solving 5 + x = 7.496665926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.496665926 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.496665926 + -5 x = 7.496665926 + -5 Combine like terms: 7.496665926 + -5 = 2.496665926 x = 2.496665926 Simplifying x = 2.496665926Subproblem 2
x + 5 = -7.496665926 Simplifying x + 5 = -7.496665926 Reorder the terms: 5 + x = -7.496665926 Solving 5 + x = -7.496665926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.496665926 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.496665926 + -5 x = -7.496665926 + -5 Combine like terms: -7.496665926 + -5 = -12.496665926 x = -12.496665926 Simplifying x = -12.496665926Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.496665926, -12.496665926}
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