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Simplifying 4.9x2 + -65x + -115 = 0 Reorder the terms: -115 + -65x + 4.9x2 = 0 Solving -115 + -65x + 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'. -23.46938776 + -13.26530612x + x2 = 0 Move the constant term to the right: Add '23.46938776' to each side of the equation. -23.46938776 + -13.26530612x + 23.46938776 + x2 = 0 + 23.46938776 Reorder the terms: -23.46938776 + 23.46938776 + -13.26530612x + x2 = 0 + 23.46938776 Combine like terms: -23.46938776 + 23.46938776 = 0.00000000 0.00000000 + -13.26530612x + x2 = 0 + 23.46938776 -13.26530612x + x2 = 0 + 23.46938776 Combine like terms: 0 + 23.46938776 = 23.46938776 -13.26530612x + x2 = 23.46938776 The x term is -13.26530612x. Take half its coefficient (-6.63265306). Square it (43.99208661) and add it to both sides. Add '43.99208661' to each side of the equation. -13.26530612x + 43.99208661 + x2 = 23.46938776 + 43.99208661 Reorder the terms: 43.99208661 + -13.26530612x + x2 = 23.46938776 + 43.99208661 Combine like terms: 23.46938776 + 43.99208661 = 67.46147437 43.99208661 + -13.26530612x + x2 = 67.46147437 Factor a perfect square on the left side: (x + -6.63265306)(x + -6.63265306) = 67.46147437 Calculate the square root of the right side: 8.213493433 Break this problem into two subproblems by setting (x + -6.63265306) equal to 8.213493433 and -8.213493433.Subproblem 1
x + -6.63265306 = 8.213493433 Simplifying x + -6.63265306 = 8.213493433 Reorder the terms: -6.63265306 + x = 8.213493433 Solving -6.63265306 + x = 8.213493433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.63265306' to each side of the equation. -6.63265306 + 6.63265306 + x = 8.213493433 + 6.63265306 Combine like terms: -6.63265306 + 6.63265306 = 0.00000000 0.00000000 + x = 8.213493433 + 6.63265306 x = 8.213493433 + 6.63265306 Combine like terms: 8.213493433 + 6.63265306 = 14.846146493 x = 14.846146493 Simplifying x = 14.846146493Subproblem 2
x + -6.63265306 = -8.213493433 Simplifying x + -6.63265306 = -8.213493433 Reorder the terms: -6.63265306 + x = -8.213493433 Solving -6.63265306 + x = -8.213493433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.63265306' to each side of the equation. -6.63265306 + 6.63265306 + x = -8.213493433 + 6.63265306 Combine like terms: -6.63265306 + 6.63265306 = 0.00000000 0.00000000 + x = -8.213493433 + 6.63265306 x = -8.213493433 + 6.63265306 Combine like terms: -8.213493433 + 6.63265306 = -1.580840373 x = -1.580840373 Simplifying x = -1.580840373Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.846146493, -1.580840373}
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