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Simplifying 35x2 + 175x + -160 = 0 Reorder the terms: -160 + 175x + 35x2 = 0 Solving -160 + 175x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-32 + 35x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-32 + 35x + 7x2)' equal to zero and attempt to solve: Simplifying -32 + 35x + 7x2 = 0 Solving -32 + 35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + 5x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + 5x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + 5x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + 5x + x2 = 0 + 4.571428571 5x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 5x + x2 = 4.571428571 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 4.571428571 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 4.571428571 + 6.25 Combine like terms: 4.571428571 + 6.25 = 10.821428571 6.25 + 5x + x2 = 10.821428571 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 10.821428571 Calculate the square root of the right side: 3.289593983 Break this problem into two subproblems by setting (x + 2.5) equal to 3.289593983 and -3.289593983.Subproblem 1
x + 2.5 = 3.289593983 Simplifying x + 2.5 = 3.289593983 Reorder the terms: 2.5 + x = 3.289593983 Solving 2.5 + x = 3.289593983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.289593983 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.289593983 + -2.5 x = 3.289593983 + -2.5 Combine like terms: 3.289593983 + -2.5 = 0.789593983 x = 0.789593983 Simplifying x = 0.789593983Subproblem 2
x + 2.5 = -3.289593983 Simplifying x + 2.5 = -3.289593983 Reorder the terms: 2.5 + x = -3.289593983 Solving 2.5 + x = -3.289593983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.289593983 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.289593983 + -2.5 x = -3.289593983 + -2.5 Combine like terms: -3.289593983 + -2.5 = -5.789593983 x = -5.789593983 Simplifying x = -5.789593983Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.789593983, -5.789593983}Solution
x = {0.789593983, -5.789593983}
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