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Simplifying 4.9x2 + 6.9x + -2.4 = 0 Reorder the terms: -2.4 + 6.9x + 4.9x2 = 0 Solving -2.4 + 6.9x + 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'. -0.4897959184 + 1.408163265x + x2 = 0 Move the constant term to the right: Add '0.4897959184' to each side of the equation. -0.4897959184 + 1.408163265x + 0.4897959184 + x2 = 0 + 0.4897959184 Reorder the terms: -0.4897959184 + 0.4897959184 + 1.408163265x + x2 = 0 + 0.4897959184 Combine like terms: -0.4897959184 + 0.4897959184 = 0.0000000000 0.0000000000 + 1.408163265x + x2 = 0 + 0.4897959184 1.408163265x + x2 = 0 + 0.4897959184 Combine like terms: 0 + 0.4897959184 = 0.4897959184 1.408163265x + x2 = 0.4897959184 The x term is 1.408163265x. Take half its coefficient (0.7040816325). Square it (0.4957309452) and add it to both sides. Add '0.4957309452' to each side of the equation. 1.408163265x + 0.4957309452 + x2 = 0.4897959184 + 0.4957309452 Reorder the terms: 0.4957309452 + 1.408163265x + x2 = 0.4897959184 + 0.4957309452 Combine like terms: 0.4897959184 + 0.4957309452 = 0.9855268636 0.4957309452 + 1.408163265x + x2 = 0.9855268636 Factor a perfect square on the left side: (x + 0.7040816325)(x + 0.7040816325) = 0.9855268636 Calculate the square root of the right side: 0.992737057 Break this problem into two subproblems by setting (x + 0.7040816325) equal to 0.992737057 and -0.992737057.Subproblem 1
x + 0.7040816325 = 0.992737057 Simplifying x + 0.7040816325 = 0.992737057 Reorder the terms: 0.7040816325 + x = 0.992737057 Solving 0.7040816325 + x = 0.992737057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7040816325' to each side of the equation. 0.7040816325 + -0.7040816325 + x = 0.992737057 + -0.7040816325 Combine like terms: 0.7040816325 + -0.7040816325 = 0.0000000000 0.0000000000 + x = 0.992737057 + -0.7040816325 x = 0.992737057 + -0.7040816325 Combine like terms: 0.992737057 + -0.7040816325 = 0.2886554245 x = 0.2886554245 Simplifying x = 0.2886554245Subproblem 2
x + 0.7040816325 = -0.992737057 Simplifying x + 0.7040816325 = -0.992737057 Reorder the terms: 0.7040816325 + x = -0.992737057 Solving 0.7040816325 + x = -0.992737057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7040816325' to each side of the equation. 0.7040816325 + -0.7040816325 + x = -0.992737057 + -0.7040816325 Combine like terms: 0.7040816325 + -0.7040816325 = 0.0000000000 0.0000000000 + x = -0.992737057 + -0.7040816325 x = -0.992737057 + -0.7040816325 Combine like terms: -0.992737057 + -0.7040816325 = -1.6968186895 x = -1.6968186895 Simplifying x = -1.6968186895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2886554245, -1.6968186895}
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