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Simplifying -4.9x2 + 8x + 10 = 0 Reorder the terms: 10 + 8x + -4.9x2 = 0 Solving 10 + 8x + -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'. -2.040816327 + -1.632653061x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1.632653061x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1.632653061x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1.632653061x + x2 = 0 + 2.040816327 -1.632653061x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1.632653061x + x2 = 2.040816327 The x term is -1.632653061x. Take half its coefficient (-0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. -1.632653061x + 0.6663890044 + x2 = 2.040816327 + 0.6663890044 Reorder the terms: 0.6663890044 + -1.632653061x + x2 = 2.040816327 + 0.6663890044 Combine like terms: 2.040816327 + 0.6663890044 = 2.7072053314 0.6663890044 + -1.632653061x + x2 = 2.7072053314 Factor a perfect square on the left side: (x + -0.8163265305)(x + -0.8163265305) = 2.7072053314 Calculate the square root of the right side: 1.645358724 Break this problem into two subproblems by setting (x + -0.8163265305) equal to 1.645358724 and -1.645358724.Subproblem 1
x + -0.8163265305 = 1.645358724 Simplifying x + -0.8163265305 = 1.645358724 Reorder the terms: -0.8163265305 + x = 1.645358724 Solving -0.8163265305 + x = 1.645358724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + x = 1.645358724 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = 1.645358724 + 0.8163265305 x = 1.645358724 + 0.8163265305 Combine like terms: 1.645358724 + 0.8163265305 = 2.4616852545 x = 2.4616852545 Simplifying x = 2.4616852545Subproblem 2
x + -0.8163265305 = -1.645358724 Simplifying x + -0.8163265305 = -1.645358724 Reorder the terms: -0.8163265305 + x = -1.645358724 Solving -0.8163265305 + x = -1.645358724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8163265305' to each side of the equation. -0.8163265305 + 0.8163265305 + x = -1.645358724 + 0.8163265305 Combine like terms: -0.8163265305 + 0.8163265305 = 0.0000000000 0.0000000000 + x = -1.645358724 + 0.8163265305 x = -1.645358724 + 0.8163265305 Combine like terms: -1.645358724 + 0.8163265305 = -0.8290321935 x = -0.8290321935 Simplifying x = -0.8290321935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4616852545, -0.8290321935}
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