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Simplifying 5x2 + 5x + -130 = 0 Reorder the terms: -130 + 5x + 5x2 = 0 Solving -130 + 5x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-26 + x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-26 + x + x2)' equal to zero and attempt to solve: Simplifying -26 + x + x2 = 0 Solving -26 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + x + x2 = 0 + 26 x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 x + x2 = 26 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 = 26 + 0.25 Reorder the terms: 0.25 + x + x2 = 26 + 0.25 Combine like terms: 26 + 0.25 = 26.25 0.25 + x + x2 = 26.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 0.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 0.5 = 5.123475383 Simplifying x + 0.5 = 5.123475383 Reorder the terms: 0.5 + x = 5.123475383 Solving 0.5 + x = 5.123475383 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 = 5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.123475383 + -0.5 x = 5.123475383 + -0.5 Combine like terms: 5.123475383 + -0.5 = 4.623475383 x = 4.623475383 Simplifying x = 4.623475383Subproblem 2
x + 0.5 = -5.123475383 Simplifying x + 0.5 = -5.123475383 Reorder the terms: 0.5 + x = -5.123475383 Solving 0.5 + x = -5.123475383 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 = -5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.123475383 + -0.5 x = -5.123475383 + -0.5 Combine like terms: -5.123475383 + -0.5 = -5.623475383 x = -5.623475383 Simplifying x = -5.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.623475383, -5.623475383}Solution
x = {4.623475383, -5.623475383}
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