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Simplifying 0 = x2 + 5x + -15 Reorder the terms: 0 = -15 + 5x + x2 Solving 0 = -15 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + -5x + -1x2 = -15 + 5x + x2 + 15 + -5x + -1x2 Reorder the terms: 15 + -5x + -1x2 = -15 + 15 + 5x + -5x + x2 + -1x2 Combine like terms: -15 + 15 = 0 15 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 15 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 15 + -5x + -1x2 = 0 + x2 + -1x2 15 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 5x + x2 = 0 + 15 5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 5x + x2 = 15 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 = 15 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 15 + 6.25 Combine like terms: 15 + 6.25 = 21.25 6.25 + 5x + x2 = 21.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 2.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 2.5 = 4.609772229 Simplifying x + 2.5 = 4.609772229 Reorder the terms: 2.5 + x = 4.609772229 Solving 2.5 + x = 4.609772229 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 = 4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.609772229 + -2.5 x = 4.609772229 + -2.5 Combine like terms: 4.609772229 + -2.5 = 2.109772229 x = 2.109772229 Simplifying x = 2.109772229Subproblem 2
x + 2.5 = -4.609772229 Simplifying x + 2.5 = -4.609772229 Reorder the terms: 2.5 + x = -4.609772229 Solving 2.5 + x = -4.609772229 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 = -4.609772229 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.609772229 + -2.5 x = -4.609772229 + -2.5 Combine like terms: -4.609772229 + -2.5 = -7.109772229 x = -7.109772229 Simplifying x = -7.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.109772229, -7.109772229}
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