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Simplifying 5x2 + 5x = 70 Reorder the terms: 5x + 5x2 = 70 Solving 5x + 5x2 = 70 Solving for variable 'x'. Reorder the terms: -70 + 5x + 5x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-14 + x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-14 + x + x2)' equal to zero and attempt to solve: Simplifying -14 + x + x2 = 0 Solving -14 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x + x2 = 0 + 14 x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 x + x2 = 14 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. x + 0.25 + x2 = 14 + 0.25 Reorder the terms: 0.25 + x + x2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + x + x2 = 14.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 0.5 = 3.774917218 Simplifying x + 0.5 = 3.774917218 Reorder the terms: 0.5 + x = 3.774917218 Solving 0.5 + x = 3.774917218 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 = 3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.774917218 + -0.5 x = 3.774917218 + -0.5 Combine like terms: 3.774917218 + -0.5 = 3.274917218 x = 3.274917218 Simplifying x = 3.274917218Subproblem 2
x + 0.5 = -3.774917218 Simplifying x + 0.5 = -3.774917218 Reorder the terms: 0.5 + x = -3.774917218 Solving 0.5 + x = -3.774917218 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 = -3.774917218 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.774917218 + -0.5 x = -3.774917218 + -0.5 Combine like terms: -3.774917218 + -0.5 = -4.274917218 x = -4.274917218 Simplifying x = -4.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.274917218, -4.274917218}Solution
x = {3.274917218, -4.274917218}
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