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Simplifying -4.905x2 + -2.5x + 7 = 0 Reorder the terms: 7 + -2.5x + -4.905x2 = 0 Solving 7 + -2.5x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -1.427115189 + 0.5096839959x + x2 = 0 Move the constant term to the right: Add '1.427115189' to each side of the equation. -1.427115189 + 0.5096839959x + 1.427115189 + x2 = 0 + 1.427115189 Reorder the terms: -1.427115189 + 1.427115189 + 0.5096839959x + x2 = 0 + 1.427115189 Combine like terms: -1.427115189 + 1.427115189 = 0.000000000 0.000000000 + 0.5096839959x + x2 = 0 + 1.427115189 0.5096839959x + x2 = 0 + 1.427115189 Combine like terms: 0 + 1.427115189 = 1.427115189 0.5096839959x + x2 = 1.427115189 The x term is 0.5096839959x. Take half its coefficient (0.254841998). Square it (0.06494444394) and add it to both sides. Add '0.06494444394' to each side of the equation. 0.5096839959x + 0.06494444394 + x2 = 1.427115189 + 0.06494444394 Reorder the terms: 0.06494444394 + 0.5096839959x + x2 = 1.427115189 + 0.06494444394 Combine like terms: 1.427115189 + 0.06494444394 = 1.49205963294 0.06494444394 + 0.5096839959x + x2 = 1.49205963294 Factor a perfect square on the left side: (x + 0.254841998)(x + 0.254841998) = 1.49205963294 Calculate the square root of the right side: 1.221498929 Break this problem into two subproblems by setting (x + 0.254841998) equal to 1.221498929 and -1.221498929.Subproblem 1
x + 0.254841998 = 1.221498929 Simplifying x + 0.254841998 = 1.221498929 Reorder the terms: 0.254841998 + x = 1.221498929 Solving 0.254841998 + x = 1.221498929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.254841998' to each side of the equation. 0.254841998 + -0.254841998 + x = 1.221498929 + -0.254841998 Combine like terms: 0.254841998 + -0.254841998 = 0.000000000 0.000000000 + x = 1.221498929 + -0.254841998 x = 1.221498929 + -0.254841998 Combine like terms: 1.221498929 + -0.254841998 = 0.966656931 x = 0.966656931 Simplifying x = 0.966656931Subproblem 2
x + 0.254841998 = -1.221498929 Simplifying x + 0.254841998 = -1.221498929 Reorder the terms: 0.254841998 + x = -1.221498929 Solving 0.254841998 + x = -1.221498929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.254841998' to each side of the equation. 0.254841998 + -0.254841998 + x = -1.221498929 + -0.254841998 Combine like terms: 0.254841998 + -0.254841998 = 0.000000000 0.000000000 + x = -1.221498929 + -0.254841998 x = -1.221498929 + -0.254841998 Combine like terms: -1.221498929 + -0.254841998 = -1.476340927 x = -1.476340927 Simplifying x = -1.476340927Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.966656931, -1.476340927}
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