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Simplifying 3x2 + 15x + -100 = 0 Reorder the terms: -100 + 15x + 3x2 = 0 Solving -100 + 15x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33.33333333 + 5x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 5x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 5x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 5x + x2 = 0 + 33.33333333 5x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 5x + x2 = 33.33333333 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 = 33.33333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 33.33333333 + 6.25 Combine like terms: 33.33333333 + 6.25 = 39.58333333 6.25 + 5x + x2 = 39.58333333 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 39.58333333 Calculate the square root of the right side: 6.291528696 Break this problem into two subproblems by setting (x + 2.5) equal to 6.291528696 and -6.291528696.Subproblem 1
x + 2.5 = 6.291528696 Simplifying x + 2.5 = 6.291528696 Reorder the terms: 2.5 + x = 6.291528696 Solving 2.5 + x = 6.291528696 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 = 6.291528696 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.291528696 + -2.5 x = 6.291528696 + -2.5 Combine like terms: 6.291528696 + -2.5 = 3.791528696 x = 3.791528696 Simplifying x = 3.791528696Subproblem 2
x + 2.5 = -6.291528696 Simplifying x + 2.5 = -6.291528696 Reorder the terms: 2.5 + x = -6.291528696 Solving 2.5 + x = -6.291528696 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 = -6.291528696 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.291528696 + -2.5 x = -6.291528696 + -2.5 Combine like terms: -6.291528696 + -2.5 = -8.791528696 x = -8.791528696 Simplifying x = -8.791528696Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.791528696, -8.791528696}
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