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Simplifying 95 = -5x(-6x + -7) Reorder the terms: 95 = -5x(-7 + -6x) 95 = (-7 * -5x + -6x * -5x) 95 = (35x + 30x2) Solving 95 = 35x + 30x2 Solving for variable 'x'. Reorder the terms: 95 + -35x + -30x2 = 35x + -35x + 30x2 + -30x2 Combine like terms: 35x + -35x = 0 95 + -35x + -30x2 = 0 + 30x2 + -30x2 95 + -35x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 95 + -35x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(19 + -7x + -6x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(19 + -7x + -6x2)' equal to zero and attempt to solve: Simplifying 19 + -7x + -6x2 = 0 Solving 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 = 1.2893504215 x = 1.2893504215 Simplifying x = 1.2893504215Subproblem 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 = -2.4560170885 x = -2.4560170885 Simplifying x = -2.4560170885Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2893504215, -2.4560170885}Solution
x = {1.2893504215, -2.4560170885}
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