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Simplifying 2x2 + 30x + 2 = 0 Reorder the terms: 2 + 30x + 2x2 = 0 Solving 2 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 15x + x2)' equal to zero and attempt to solve: Simplifying 1 + 15x + x2 = 0 Solving 1 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 15x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 15x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 15x + x2 = 0 + -1 15x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 15x + x2 = -1 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -1 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -1 + 56.25 Combine like terms: -1 + 56.25 = 55.25 56.25 + 15x + x2 = 55.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 7.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 7.5 = 7.433034374 Simplifying x + 7.5 = 7.433034374 Reorder the terms: 7.5 + x = 7.433034374 Solving 7.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.433034374 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.433034374 + -7.5 x = 7.433034374 + -7.5 Combine like terms: 7.433034374 + -7.5 = -0.066965626 x = -0.066965626 Simplifying x = -0.066965626Subproblem 2
x + 7.5 = -7.433034374 Simplifying x + 7.5 = -7.433034374 Reorder the terms: 7.5 + x = -7.433034374 Solving 7.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.433034374 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.433034374 + -7.5 x = -7.433034374 + -7.5 Combine like terms: -7.433034374 + -7.5 = -14.933034374 x = -14.933034374 Simplifying x = -14.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.066965626, -14.933034374}Solution
x = {-0.066965626, -14.933034374}
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