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Simplifying 2x2 + 18x + -14 = 0 Reorder the terms: -14 + 18x + 2x2 = 0 Solving -14 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 9x + x2)' equal to zero and attempt to solve: Simplifying -7 + 9x + x2 = 0 Solving -7 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 9x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 9x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 9x + x2 = 0 + 7 9x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 9x + x2 = 7 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 7 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + 9x + x2 = 27.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 4.5 = 5.220153254 Simplifying x + 4.5 = 5.220153254 Reorder the terms: 4.5 + x = 5.220153254 Solving 4.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.220153254 + -4.5 x = 5.220153254 + -4.5 Combine like terms: 5.220153254 + -4.5 = 0.720153254 x = 0.720153254 Simplifying x = 0.720153254Subproblem 2
x + 4.5 = -5.220153254 Simplifying x + 4.5 = -5.220153254 Reorder the terms: 4.5 + x = -5.220153254 Solving 4.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.220153254 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.220153254 + -4.5 x = -5.220153254 + -4.5 Combine like terms: -5.220153254 + -4.5 = -9.720153254 x = -9.720153254 Simplifying x = -9.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.720153254, -9.720153254}Solution
x = {0.720153254, -9.720153254}
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