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Simplifying -4.9x2 + 9x + 600 = 0 Reorder the terms: 600 + 9x + -4.9x2 = 0 Solving 600 + 9x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -122.4489796 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -1.836734694x + 122.4489796 + x2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -1.836734694x + x2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -1.836734694x + x2 = 0 + 122.4489796 -1.836734694x + x2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -1.836734694x + x2 = 122.4489796 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 122.4489796 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 122.4489796 + 0.8433985840 Combine like terms: 122.4489796 + 0.8433985840 = 123.292378184 0.8433985840 + -1.836734694x + x2 = 123.292378184 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 123.292378184 Calculate the square root of the right side: 11.103710109 Break this problem into two subproblems by setting (x + -0.918367347) equal to 11.103710109 and -11.103710109.Subproblem 1
x + -0.918367347 = 11.103710109 Simplifying x + -0.918367347 = 11.103710109 Reorder the terms: -0.918367347 + x = 11.103710109 Solving -0.918367347 + x = 11.103710109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 11.103710109 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 11.103710109 + 0.918367347 x = 11.103710109 + 0.918367347 Combine like terms: 11.103710109 + 0.918367347 = 12.022077456 x = 12.022077456 Simplifying x = 12.022077456Subproblem 2
x + -0.918367347 = -11.103710109 Simplifying x + -0.918367347 = -11.103710109 Reorder the terms: -0.918367347 + x = -11.103710109 Solving -0.918367347 + x = -11.103710109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -11.103710109 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -11.103710109 + 0.918367347 x = -11.103710109 + 0.918367347 Combine like terms: -11.103710109 + 0.918367347 = -10.185342762 x = -10.185342762 Simplifying x = -10.185342762Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.022077456, -10.185342762}
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