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Simplifying -4.9x2 + 2.5x + 5 = 0 Reorder the terms: 5 + 2.5x + -4.9x2 = 0 Solving 5 + 2.5x + -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'. -1.020408163 + -0.5102040816x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -0.5102040816x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -0.5102040816x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -0.5102040816x + x2 = 0 + 1.020408163 -0.5102040816x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -0.5102040816x + x2 = 1.020408163 The x term is -0.5102040816x. Take half its coefficient (-0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. -0.5102040816x + 0.06507705122 + x2 = 1.020408163 + 0.06507705122 Reorder the terms: 0.06507705122 + -0.5102040816x + x2 = 1.020408163 + 0.06507705122 Combine like terms: 1.020408163 + 0.06507705122 = 1.08548521422 0.06507705122 + -0.5102040816x + x2 = 1.08548521422 Factor a perfect square on the left side: (x + -0.2551020408)(x + -0.2551020408) = 1.08548521422 Calculate the square root of the right side: 1.041866217 Break this problem into two subproblems by setting (x + -0.2551020408) equal to 1.041866217 and -1.041866217.Subproblem 1
x + -0.2551020408 = 1.041866217 Simplifying x + -0.2551020408 = 1.041866217 Reorder the terms: -0.2551020408 + x = 1.041866217 Solving -0.2551020408 + x = 1.041866217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + x = 1.041866217 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + x = 1.041866217 + 0.2551020408 x = 1.041866217 + 0.2551020408 Combine like terms: 1.041866217 + 0.2551020408 = 1.2969682578 x = 1.2969682578 Simplifying x = 1.2969682578Subproblem 2
x + -0.2551020408 = -1.041866217 Simplifying x + -0.2551020408 = -1.041866217 Reorder the terms: -0.2551020408 + x = -1.041866217 Solving -0.2551020408 + x = -1.041866217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + x = -1.041866217 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + x = -1.041866217 + 0.2551020408 x = -1.041866217 + 0.2551020408 Combine like terms: -1.041866217 + 0.2551020408 = -0.7867641762 x = -0.7867641762 Simplifying x = -0.7867641762Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2969682578, -0.7867641762}
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