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Simplifying 2x2 + -3x + -100 = 0 Reorder the terms: -100 + -3x + 2x2 = 0 Solving -100 + -3x + 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'. -50 + -1.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -1.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -1.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -1.5x + x2 = 0 + 50 -1.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -1.5x + x2 = 50 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 50 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 50 + 0.5625 Combine like terms: 50 + 0.5625 = 50.5625 0.5625 + -1.5x + x2 = 50.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 50.5625 Calculate the square root of the right side: 7.110731327 Break this problem into two subproblems by setting (x + -0.75) equal to 7.110731327 and -7.110731327.Subproblem 1
x + -0.75 = 7.110731327 Simplifying x + -0.75 = 7.110731327 Reorder the terms: -0.75 + x = 7.110731327 Solving -0.75 + x = 7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 7.110731327 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 7.110731327 + 0.75 x = 7.110731327 + 0.75 Combine like terms: 7.110731327 + 0.75 = 7.860731327 x = 7.860731327 Simplifying x = 7.860731327Subproblem 2
x + -0.75 = -7.110731327 Simplifying x + -0.75 = -7.110731327 Reorder the terms: -0.75 + x = -7.110731327 Solving -0.75 + x = -7.110731327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -7.110731327 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -7.110731327 + 0.75 x = -7.110731327 + 0.75 Combine like terms: -7.110731327 + 0.75 = -6.360731327 x = -6.360731327 Simplifying x = -6.360731327Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.860731327, -6.360731327}
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