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Simplifying 0 = 4.9x2 + 12x + -91 Reorder the terms: 0 = -91 + 12x + 4.9x2 Solving 0 = -91 + 12x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 91 = 91 91 + -12x + -4.9x2 = -91 + 12x + 4.9x2 + 91 + -12x + -4.9x2 Reorder the terms: 91 + -12x + -4.9x2 = -91 + 91 + 12x + -12x + 4.9x2 + -4.9x2 Combine like terms: -91 + 91 = 0 91 + -12x + -4.9x2 = 0 + 12x + -12x + 4.9x2 + -4.9x2 91 + -12x + -4.9x2 = 12x + -12x + 4.9x2 + -4.9x2 Combine like terms: 12x + -12x = 0 91 + -12x + -4.9x2 = 0 + 4.9x2 + -4.9x2 91 + -12x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 91 + -12x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -18.57142857 + 2.448979592x + x2 = 0 Move the constant term to the right: Add '18.57142857' to each side of the equation. -18.57142857 + 2.448979592x + 18.57142857 + x2 = 0 + 18.57142857 Reorder the terms: -18.57142857 + 18.57142857 + 2.448979592x + x2 = 0 + 18.57142857 Combine like terms: -18.57142857 + 18.57142857 = 0.00000000 0.00000000 + 2.448979592x + x2 = 0 + 18.57142857 2.448979592x + x2 = 0 + 18.57142857 Combine like terms: 0 + 18.57142857 = 18.57142857 2.448979592x + x2 = 18.57142857 The x term is 2.448979592x. Take half its coefficient (1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. 2.448979592x + 1.499375261 + x2 = 18.57142857 + 1.499375261 Reorder the terms: 1.499375261 + 2.448979592x + x2 = 18.57142857 + 1.499375261 Combine like terms: 18.57142857 + 1.499375261 = 20.070803831 1.499375261 + 2.448979592x + x2 = 20.070803831 Factor a perfect square on the left side: (x + 1.224489796)(x + 1.224489796) = 20.070803831 Calculate the square root of the right side: 4.48004507 Break this problem into two subproblems by setting (x + 1.224489796) equal to 4.48004507 and -4.48004507.Subproblem 1
x + 1.224489796 = 4.48004507 Simplifying x + 1.224489796 = 4.48004507 Reorder the terms: 1.224489796 + x = 4.48004507 Solving 1.224489796 + x = 4.48004507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + x = 4.48004507 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = 4.48004507 + -1.224489796 x = 4.48004507 + -1.224489796 Combine like terms: 4.48004507 + -1.224489796 = 3.255555274 x = 3.255555274 Simplifying x = 3.255555274Subproblem 2
x + 1.224489796 = -4.48004507 Simplifying x + 1.224489796 = -4.48004507 Reorder the terms: 1.224489796 + x = -4.48004507 Solving 1.224489796 + x = -4.48004507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.224489796' to each side of the equation. 1.224489796 + -1.224489796 + x = -4.48004507 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + x = -4.48004507 + -1.224489796 x = -4.48004507 + -1.224489796 Combine like terms: -4.48004507 + -1.224489796 = -5.704534866 x = -5.704534866 Simplifying x = -5.704534866Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.255555274, -5.704534866}
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