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Simplifying 1.4x + -3.9x2 = -2.7 Solving 1.4x + -3.9x2 = -2.7 Solving for variable 'x'. Reorder the terms: 2.7 + 1.4x + -3.9x2 = -2.7 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 2.7 + 1.4x + -3.9x2 = 0.0 Begin completing the square. Divide all terms by -3.9 the coefficient of the squared term: Divide each side by '-3.9'. -0.6923076923 + -0.358974359x + x2 = 0 Move the constant term to the right: Add '0.6923076923' to each side of the equation. -0.6923076923 + -0.358974359x + 0.6923076923 + x2 = 0 + 0.6923076923 Reorder the terms: -0.6923076923 + 0.6923076923 + -0.358974359x + x2 = 0 + 0.6923076923 Combine like terms: -0.6923076923 + 0.6923076923 = 0.0000000000 0.0000000000 + -0.358974359x + x2 = 0 + 0.6923076923 -0.358974359x + x2 = 0 + 0.6923076923 Combine like terms: 0 + 0.6923076923 = 0.6923076923 -0.358974359x + x2 = 0.6923076923 The x term is -0.358974359x. Take half its coefficient (-0.1794871795). Square it (0.03221564760) and add it to both sides. Add '0.03221564760' to each side of the equation. -0.358974359x + 0.03221564760 + x2 = 0.6923076923 + 0.03221564760 Reorder the terms: 0.03221564760 + -0.358974359x + x2 = 0.6923076923 + 0.03221564760 Combine like terms: 0.6923076923 + 0.03221564760 = 0.7245233399 0.03221564760 + -0.358974359x + x2 = 0.7245233399 Factor a perfect square on the left side: (x + -0.1794871795)(x + -0.1794871795) = 0.7245233399 Calculate the square root of the right side: 0.851189368 Break this problem into two subproblems by setting (x + -0.1794871795) equal to 0.851189368 and -0.851189368.Subproblem 1
x + -0.1794871795 = 0.851189368 Simplifying x + -0.1794871795 = 0.851189368 Reorder the terms: -0.1794871795 + x = 0.851189368 Solving -0.1794871795 + x = 0.851189368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1794871795' to each side of the equation. -0.1794871795 + 0.1794871795 + x = 0.851189368 + 0.1794871795 Combine like terms: -0.1794871795 + 0.1794871795 = 0.0000000000 0.0000000000 + x = 0.851189368 + 0.1794871795 x = 0.851189368 + 0.1794871795 Combine like terms: 0.851189368 + 0.1794871795 = 1.0306765475 x = 1.0306765475 Simplifying x = 1.0306765475Subproblem 2
x + -0.1794871795 = -0.851189368 Simplifying x + -0.1794871795 = -0.851189368 Reorder the terms: -0.1794871795 + x = -0.851189368 Solving -0.1794871795 + x = -0.851189368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1794871795' to each side of the equation. -0.1794871795 + 0.1794871795 + x = -0.851189368 + 0.1794871795 Combine like terms: -0.1794871795 + 0.1794871795 = 0.0000000000 0.0000000000 + x = -0.851189368 + 0.1794871795 x = -0.851189368 + 0.1794871795 Combine like terms: -0.851189368 + 0.1794871795 = -0.6717021885 x = -0.6717021885 Simplifying x = -0.6717021885Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0306765475, -0.6717021885}
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