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Simplifying 7x2 + -1.9x = 6 Reorder the terms: -1.9x + 7x2 = 6 Solving -1.9x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -1.9x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -1.9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -0.2714285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.2714285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.2714285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.2714285714x + x2 = 0 + 0.8571428571 -0.2714285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.2714285714x + x2 = 0.8571428571 The x term is -0.2714285714x. Take half its coefficient (-0.1357142857). Square it (0.01841836734) and add it to both sides. Add '0.01841836734' to each side of the equation. -0.2714285714x + 0.01841836734 + x2 = 0.8571428571 + 0.01841836734 Reorder the terms: 0.01841836734 + -0.2714285714x + x2 = 0.8571428571 + 0.01841836734 Combine like terms: 0.8571428571 + 0.01841836734 = 0.87556122444 0.01841836734 + -0.2714285714x + x2 = 0.87556122444 Factor a perfect square on the left side: (x + -0.1357142857)(x + -0.1357142857) = 0.87556122444 Calculate the square root of the right side: 0.935714286 Break this problem into two subproblems by setting (x + -0.1357142857) equal to 0.935714286 and -0.935714286.Subproblem 1
x + -0.1357142857 = 0.935714286 Simplifying x + -0.1357142857 = 0.935714286 Reorder the terms: -0.1357142857 + x = 0.935714286 Solving -0.1357142857 + x = 0.935714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1357142857' to each side of the equation. -0.1357142857 + 0.1357142857 + x = 0.935714286 + 0.1357142857 Combine like terms: -0.1357142857 + 0.1357142857 = 0.0000000000 0.0000000000 + x = 0.935714286 + 0.1357142857 x = 0.935714286 + 0.1357142857 Combine like terms: 0.935714286 + 0.1357142857 = 1.0714285717 x = 1.0714285717 Simplifying x = 1.0714285717Subproblem 2
x + -0.1357142857 = -0.935714286 Simplifying x + -0.1357142857 = -0.935714286 Reorder the terms: -0.1357142857 + x = -0.935714286 Solving -0.1357142857 + x = -0.935714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1357142857' to each side of the equation. -0.1357142857 + 0.1357142857 + x = -0.935714286 + 0.1357142857 Combine like terms: -0.1357142857 + 0.1357142857 = 0.0000000000 0.0000000000 + x = -0.935714286 + 0.1357142857 x = -0.935714286 + 0.1357142857 Combine like terms: -0.935714286 + 0.1357142857 = -0.8000000003 x = -0.8000000003 Simplifying x = -0.8000000003Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0714285717, -0.8000000003}
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