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Simplifying -4.9x2 + 238x + 381 = 0 Reorder the terms: 381 + 238x + -4.9x2 = 0 Solving 381 + 238x + -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'. -77.75510204 + -48.57142857x + x2 = 0 Move the constant term to the right: Add '77.75510204' to each side of the equation. -77.75510204 + -48.57142857x + 77.75510204 + x2 = 0 + 77.75510204 Reorder the terms: -77.75510204 + 77.75510204 + -48.57142857x + x2 = 0 + 77.75510204 Combine like terms: -77.75510204 + 77.75510204 = 0.00000000 0.00000000 + -48.57142857x + x2 = 0 + 77.75510204 -48.57142857x + x2 = 0 + 77.75510204 Combine like terms: 0 + 77.75510204 = 77.75510204 -48.57142857x + x2 = 77.75510204 The x term is -48.57142857x. Take half its coefficient (-24.28571429). Square it (589.7959186) and add it to both sides. Add '589.7959186' to each side of the equation. -48.57142857x + 589.7959186 + x2 = 77.75510204 + 589.7959186 Reorder the terms: 589.7959186 + -48.57142857x + x2 = 77.75510204 + 589.7959186 Combine like terms: 77.75510204 + 589.7959186 = 667.55102064 589.7959186 + -48.57142857x + x2 = 667.55102064 Factor a perfect square on the left side: (x + -24.28571429)(x + -24.28571429) = 667.55102064 Calculate the square root of the right side: 25.83700874 Break this problem into two subproblems by setting (x + -24.28571429) equal to 25.83700874 and -25.83700874.Subproblem 1
x + -24.28571429 = 25.83700874 Simplifying x + -24.28571429 = 25.83700874 Reorder the terms: -24.28571429 + x = 25.83700874 Solving -24.28571429 + x = 25.83700874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.28571429' to each side of the equation. -24.28571429 + 24.28571429 + x = 25.83700874 + 24.28571429 Combine like terms: -24.28571429 + 24.28571429 = 0.00000000 0.00000000 + x = 25.83700874 + 24.28571429 x = 25.83700874 + 24.28571429 Combine like terms: 25.83700874 + 24.28571429 = 50.12272303 x = 50.12272303 Simplifying x = 50.12272303Subproblem 2
x + -24.28571429 = -25.83700874 Simplifying x + -24.28571429 = -25.83700874 Reorder the terms: -24.28571429 + x = -25.83700874 Solving -24.28571429 + x = -25.83700874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.28571429' to each side of the equation. -24.28571429 + 24.28571429 + x = -25.83700874 + 24.28571429 Combine like terms: -24.28571429 + 24.28571429 = 0.00000000 0.00000000 + x = -25.83700874 + 24.28571429 x = -25.83700874 + 24.28571429 Combine like terms: -25.83700874 + 24.28571429 = -1.55129445 x = -1.55129445 Simplifying x = -1.55129445Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.12272303, -1.55129445}
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