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Simplifying 3x2 + -12x + -1987 = 0 Reorder the terms: -1987 + -12x + 3x2 = 0 Solving -1987 + -12x + 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'. -662.3333333 + -4x + x2 = 0 Move the constant term to the right: Add '662.3333333' to each side of the equation. -662.3333333 + -4x + 662.3333333 + x2 = 0 + 662.3333333 Reorder the terms: -662.3333333 + 662.3333333 + -4x + x2 = 0 + 662.3333333 Combine like terms: -662.3333333 + 662.3333333 = 0.0000000 0.0000000 + -4x + x2 = 0 + 662.3333333 -4x + x2 = 0 + 662.3333333 Combine like terms: 0 + 662.3333333 = 662.3333333 -4x + x2 = 662.3333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 662.3333333 + 4 Reorder the terms: 4 + -4x + x2 = 662.3333333 + 4 Combine like terms: 662.3333333 + 4 = 666.3333333 4 + -4x + x2 = 666.3333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 666.3333333 Calculate the square root of the right side: 25.813433195 Break this problem into two subproblems by setting (x + -2) equal to 25.813433195 and -25.813433195.Subproblem 1
x + -2 = 25.813433195 Simplifying x + -2 = 25.813433195 Reorder the terms: -2 + x = 25.813433195 Solving -2 + x = 25.813433195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 25.813433195 + 2 Combine like terms: -2 + 2 = 0 0 + x = 25.813433195 + 2 x = 25.813433195 + 2 Combine like terms: 25.813433195 + 2 = 27.813433195 x = 27.813433195 Simplifying x = 27.813433195Subproblem 2
x + -2 = -25.813433195 Simplifying x + -2 = -25.813433195 Reorder the terms: -2 + x = -25.813433195 Solving -2 + x = -25.813433195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -25.813433195 + 2 Combine like terms: -2 + 2 = 0 0 + x = -25.813433195 + 2 x = -25.813433195 + 2 Combine like terms: -25.813433195 + 2 = -23.813433195 x = -23.813433195 Simplifying x = -23.813433195Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.813433195, -23.813433195}
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