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Simplifying -4.9x2 + 7.25x + -1.25 = 0 Reorder the terms: -1.25 + 7.25x + -4.9x2 = 0 Solving -1.25 + 7.25x + -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'. 0.2551020408 + -1.479591837x + x2 = 0 Move the constant term to the right: Add '-0.2551020408' to each side of the equation. 0.2551020408 + -1.479591837x + -0.2551020408 + x2 = 0 + -0.2551020408 Reorder the terms: 0.2551020408 + -0.2551020408 + -1.479591837x + x2 = 0 + -0.2551020408 Combine like terms: 0.2551020408 + -0.2551020408 = 0.0000000000 0.0000000000 + -1.479591837x + x2 = 0 + -0.2551020408 -1.479591837x + x2 = 0 + -0.2551020408 Combine like terms: 0 + -0.2551020408 = -0.2551020408 -1.479591837x + x2 = -0.2551020408 The x term is -1.479591837x. Take half its coefficient (-0.7397959185). Square it (0.5472980010) and add it to both sides. Add '0.5472980010' to each side of the equation. -1.479591837x + 0.5472980010 + x2 = -0.2551020408 + 0.5472980010 Reorder the terms: 0.5472980010 + -1.479591837x + x2 = -0.2551020408 + 0.5472980010 Combine like terms: -0.2551020408 + 0.5472980010 = 0.2921959602 0.5472980010 + -1.479591837x + x2 = 0.2921959602 Factor a perfect square on the left side: (x + -0.7397959185)(x + -0.7397959185) = 0.2921959602 Calculate the square root of the right side: 0.540551533 Break this problem into two subproblems by setting (x + -0.7397959185) equal to 0.540551533 and -0.540551533.Subproblem 1
x + -0.7397959185 = 0.540551533 Simplifying x + -0.7397959185 = 0.540551533 Reorder the terms: -0.7397959185 + x = 0.540551533 Solving -0.7397959185 + x = 0.540551533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7397959185' to each side of the equation. -0.7397959185 + 0.7397959185 + x = 0.540551533 + 0.7397959185 Combine like terms: -0.7397959185 + 0.7397959185 = 0.0000000000 0.0000000000 + x = 0.540551533 + 0.7397959185 x = 0.540551533 + 0.7397959185 Combine like terms: 0.540551533 + 0.7397959185 = 1.2803474515 x = 1.2803474515 Simplifying x = 1.2803474515Subproblem 2
x + -0.7397959185 = -0.540551533 Simplifying x + -0.7397959185 = -0.540551533 Reorder the terms: -0.7397959185 + x = -0.540551533 Solving -0.7397959185 + x = -0.540551533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7397959185' to each side of the equation. -0.7397959185 + 0.7397959185 + x = -0.540551533 + 0.7397959185 Combine like terms: -0.7397959185 + 0.7397959185 = 0.0000000000 0.0000000000 + x = -0.540551533 + 0.7397959185 x = -0.540551533 + 0.7397959185 Combine like terms: -0.540551533 + 0.7397959185 = 0.1992443855 x = 0.1992443855 Simplifying x = 0.1992443855Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2803474515, 0.1992443855}
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