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Simplifying (5x2 + -7x + -50) + (7x2 + 9x) = 0 Reorder the terms: (-50 + -7x + 5x2) + (7x2 + 9x) = 0 Remove parenthesis around (-50 + -7x + 5x2) -50 + -7x + 5x2 + (7x2 + 9x) = 0 Reorder the terms: -50 + -7x + 5x2 + (9x + 7x2) = 0 Remove parenthesis around (9x + 7x2) -50 + -7x + 5x2 + 9x + 7x2 = 0 Reorder the terms: -50 + -7x + 9x + 5x2 + 7x2 = 0 Combine like terms: -7x + 9x = 2x -50 + 2x + 5x2 + 7x2 = 0 Combine like terms: 5x2 + 7x2 = 12x2 -50 + 2x + 12x2 = 0 Solving -50 + 2x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + x + 6x2)' equal to zero and attempt to solve: Simplifying -25 + x + 6x2 = 0 Solving -25 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.166666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 0.1666666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 0.1666666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 4.166666667 0.1666666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 0.1666666667x + x2 = 4.166666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = 4.166666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 4.166666667 + 0.25 Combine like terms: 4.166666667 + 0.25 = 4.416666667 0.25 + 0.1666666667x + x2 = 4.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.416666667 Calculate the square root of the right side: 2.101586702 Break this problem into two subproblems by setting (x + 0.5) equal to 2.101586702 and -2.101586702.Subproblem 1
x + 0.5 = 2.101586702 Simplifying x + 0.5 = 2.101586702 Reorder the terms: 0.5 + x = 2.101586702 Solving 0.5 + x = 2.101586702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.101586702 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.101586702 + -0.5 x = 2.101586702 + -0.5 Combine like terms: 2.101586702 + -0.5 = 1.601586702 x = 1.601586702 Simplifying x = 1.601586702Subproblem 2
x + 0.5 = -2.101586702 Simplifying x + 0.5 = -2.101586702 Reorder the terms: 0.5 + x = -2.101586702 Solving 0.5 + x = -2.101586702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.101586702 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.101586702 + -0.5 x = -2.101586702 + -0.5 Combine like terms: -2.101586702 + -0.5 = -2.601586702 x = -2.601586702 Simplifying x = -2.601586702Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.601586702, -2.601586702}Solution
x = {1.601586702, -2.601586702}
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