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Simplifying 0 = 2x2 + -18x + -14 Reorder the terms: 0 = -14 + -18x + 2x2 Solving 0 = -14 + -18x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 18x + -2x2 = -14 + -18x + 2x2 + 14 + 18x + -2x2 Reorder the terms: 14 + 18x + -2x2 = -14 + 14 + -18x + 18x + 2x2 + -2x2 Combine like terms: -14 + 14 = 0 14 + 18x + -2x2 = 0 + -18x + 18x + 2x2 + -2x2 14 + 18x + -2x2 = -18x + 18x + 2x2 + -2x2 Combine like terms: -18x + 18x = 0 14 + 18x + -2x2 = 0 + 2x2 + -2x2 14 + 18x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + 18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 9x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 7 + 9x + -1x2 = 0 Solving 7 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -9x + x2 = 0 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 = 9.720153254 x = 9.720153254 Simplifying x = 9.720153254Subproblem 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 = -0.720153254 x = -0.720153254 Simplifying x = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.720153254, -0.720153254}Solution
x = {9.720153254, -0.720153254}
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