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Simplifying -7x2 + -18x + 89 = 0 Reorder the terms: 89 + -18x + -7x2 = 0 Solving 89 + -18x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -12.71428571 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '12.71428571' to each side of the equation. -12.71428571 + 2.571428571x + 12.71428571 + x2 = 0 + 12.71428571 Reorder the terms: -12.71428571 + 12.71428571 + 2.571428571x + x2 = 0 + 12.71428571 Combine like terms: -12.71428571 + 12.71428571 = 0.00000000 0.00000000 + 2.571428571x + x2 = 0 + 12.71428571 2.571428571x + x2 = 0 + 12.71428571 Combine like terms: 0 + 12.71428571 = 12.71428571 2.571428571x + x2 = 12.71428571 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = 12.71428571 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 12.71428571 + 1.653061225 Combine like terms: 12.71428571 + 1.653061225 = 14.367346935 1.653061225 + 2.571428571x + x2 = 14.367346935 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 14.367346935 Calculate the square root of the right side: 3.790428331 Break this problem into two subproblems by setting (x + 1.285714286) equal to 3.790428331 and -3.790428331.Subproblem 1
x + 1.285714286 = 3.790428331 Simplifying x + 1.285714286 = 3.790428331 Reorder the terms: 1.285714286 + x = 3.790428331 Solving 1.285714286 + x = 3.790428331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 3.790428331 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 3.790428331 + -1.285714286 x = 3.790428331 + -1.285714286 Combine like terms: 3.790428331 + -1.285714286 = 2.504714045 x = 2.504714045 Simplifying x = 2.504714045Subproblem 2
x + 1.285714286 = -3.790428331 Simplifying x + 1.285714286 = -3.790428331 Reorder the terms: 1.285714286 + x = -3.790428331 Solving 1.285714286 + x = -3.790428331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -3.790428331 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -3.790428331 + -1.285714286 x = -3.790428331 + -1.285714286 Combine like terms: -3.790428331 + -1.285714286 = -5.076142617 x = -5.076142617 Simplifying x = -5.076142617Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.504714045, -5.076142617}
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