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Simplifying 15 = 2x2 + 5x + -9 Reorder the terms: 15 = -9 + 5x + 2x2 Solving 15 = -9 + 5x + 2x2 Solving for variable 'x'. Combine like terms: 15 + 9 = 24 24 + -5x + -2x2 = -9 + 5x + 2x2 + 9 + -5x + -2x2 Reorder the terms: 24 + -5x + -2x2 = -9 + 9 + 5x + -5x + 2x2 + -2x2 Combine like terms: -9 + 9 = 0 24 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2 24 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 24 + -5x + -2x2 = 0 + 2x2 + -2x2 24 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 24 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12 + 2.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 2.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 2.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2.5x + x2 = 0 + 12 2.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 2.5x + x2 = 12 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 12 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 12 + 1.5625 Combine like terms: 12 + 1.5625 = 13.5625 1.5625 + 2.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 1.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 1.25 = 3.682729966 Simplifying x + 1.25 = 3.682729966 Reorder the terms: 1.25 + x = 3.682729966 Solving 1.25 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.682729966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.682729966 + -1.25 x = 3.682729966 + -1.25 Combine like terms: 3.682729966 + -1.25 = 2.432729966 x = 2.432729966 Simplifying x = 2.432729966Subproblem 2
x + 1.25 = -3.682729966 Simplifying x + 1.25 = -3.682729966 Reorder the terms: 1.25 + x = -3.682729966 Solving 1.25 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.682729966 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.682729966 + -1.25 x = -3.682729966 + -1.25 Combine like terms: -3.682729966 + -1.25 = -4.932729966 x = -4.932729966 Simplifying x = -4.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.432729966, -4.932729966}
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