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Simplifying 3x2 + -7x + -1.2 = 0 Reorder the terms: -1.2 + -7x + 3x2 = 0 Solving -1.2 + -7x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.4 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.333333333x + x2 = 0 + 0.4 -2.333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.333333333x + x2 = 0.4 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 0.4 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 0.4 + 1.361111112 Combine like terms: 0.4 + 1.361111112 = 1.761111112 1.361111112 + -2.333333333x + x2 = 1.761111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 1.761111112 Calculate the square root of the right side: 1.327068616 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.327068616 and -1.327068616.Subproblem 1
x + -1.166666667 = 1.327068616 Simplifying x + -1.166666667 = 1.327068616 Reorder the terms: -1.166666667 + x = 1.327068616 Solving -1.166666667 + x = 1.327068616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.327068616 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.327068616 + 1.166666667 x = 1.327068616 + 1.166666667 Combine like terms: 1.327068616 + 1.166666667 = 2.493735283 x = 2.493735283 Simplifying x = 2.493735283Subproblem 2
x + -1.166666667 = -1.327068616 Simplifying x + -1.166666667 = -1.327068616 Reorder the terms: -1.166666667 + x = -1.327068616 Solving -1.166666667 + x = -1.327068616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.327068616 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.327068616 + 1.166666667 x = -1.327068616 + 1.166666667 Combine like terms: -1.327068616 + 1.166666667 = -0.160401949 x = -0.160401949 Simplifying x = -0.160401949Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.493735283, -0.160401949}
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