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Simplifying -5x2 + -35x + 10 = 0 Reorder the terms: 10 + -35x + -5x2 = 0 Solving 10 + -35x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -7x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -7x + -1x2 = 0 Solving 2 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 7x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 7x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 7x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x + x2 = 0 + 2 7x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 7x + x2 = 2 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 2 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + 7x + x2 = 14.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 3.5 = 3.774917218 Simplifying x + 3.5 = 3.774917218 Reorder the terms: 3.5 + x = 3.774917218 Solving 3.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.774917218 + -3.5 x = 3.774917218 + -3.5 Combine like terms: 3.774917218 + -3.5 = 0.274917218 x = 0.274917218 Simplifying x = 0.274917218Subproblem 2
x + 3.5 = -3.774917218 Simplifying x + 3.5 = -3.774917218 Reorder the terms: 3.5 + x = -3.774917218 Solving 3.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.774917218 + -3.5 x = -3.774917218 + -3.5 Combine like terms: -3.774917218 + -3.5 = -7.274917218 x = -7.274917218 Simplifying x = -7.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.274917218, -7.274917218}Solution
x = {0.274917218, -7.274917218}
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