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Simplifying 6x2 + -7x + -10 = 9 Reorder the terms: -10 + -7x + 6x2 = 9 Solving -10 + -7x + 6x2 = 9 Solving for variable 'x'. Reorder the terms: -10 + -9 + -7x + 6x2 = 9 + -9 Combine like terms: -10 + -9 = -19 -19 + -7x + 6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -19 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.166666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '3.166666667' to each side of the equation. -3.166666667 + -1.166666667x + 3.166666667 + x2 = 0 + 3.166666667 Reorder the terms: -3.166666667 + 3.166666667 + -1.166666667x + x2 = 0 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + 3.166666667 -1.166666667x + x2 = 0 + 3.166666667 Combine like terms: 0 + 3.166666667 = 3.166666667 -1.166666667x + x2 = 3.166666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 3.166666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 3.166666667 + 0.3402777780 Combine like terms: 3.166666667 + 0.3402777780 = 3.506944445 0.3402777780 + -1.166666667x + x2 = 3.506944445 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 3.506944445 Calculate the square root of the right side: 1.872683755 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 1.872683755 and -1.872683755.Subproblem 1
x + -0.5833333335 = 1.872683755 Simplifying x + -0.5833333335 = 1.872683755 Reorder the terms: -0.5833333335 + x = 1.872683755 Solving -0.5833333335 + x = 1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 1.872683755 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 1.872683755 + 0.5833333335 x = 1.872683755 + 0.5833333335 Combine like terms: 1.872683755 + 0.5833333335 = 2.4560170885 x = 2.4560170885 Simplifying x = 2.4560170885Subproblem 2
x + -0.5833333335 = -1.872683755 Simplifying x + -0.5833333335 = -1.872683755 Reorder the terms: -0.5833333335 + x = -1.872683755 Solving -0.5833333335 + x = -1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -1.872683755 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -1.872683755 + 0.5833333335 x = -1.872683755 + 0.5833333335 Combine like terms: -1.872683755 + 0.5833333335 = -1.2893504215 x = -1.2893504215 Simplifying x = -1.2893504215Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4560170885, -1.2893504215}
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