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Simplifying 15 + 2x + -2x2 = 0 Solving 15 + 2x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -1x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1x + x2 = 0 + 7.5 -1x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1x + x2 = 7.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 7.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 7.5 + 0.25 Combine like terms: 7.5 + 0.25 = 7.75 0.25 + -1x + x2 = 7.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + -0.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + -0.5 = 2.783882181 Simplifying x + -0.5 = 2.783882181 Reorder the terms: -0.5 + x = 2.783882181 Solving -0.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.783882181 + 0.5 x = 2.783882181 + 0.5 Combine like terms: 2.783882181 + 0.5 = 3.283882181 x = 3.283882181 Simplifying x = 3.283882181Subproblem 2
x + -0.5 = -2.783882181 Simplifying x + -0.5 = -2.783882181 Reorder the terms: -0.5 + x = -2.783882181 Solving -0.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.783882181 + 0.5 x = -2.783882181 + 0.5 Combine like terms: -2.783882181 + 0.5 = -2.283882181 x = -2.283882181 Simplifying x = -2.283882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.283882181, -2.283882181}
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