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Simplifying 9x2 + -54x = -69 Reorder the terms: -54x + 9x2 = -69 Solving -54x + 9x2 = -69 Solving for variable 'x'. Reorder the terms: 69 + -54x + 9x2 = -69 + 69 Combine like terms: -69 + 69 = 0 69 + -54x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(23 + -18x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(23 + -18x + 3x2)' equal to zero and attempt to solve: Simplifying 23 + -18x + 3x2 = 0 Solving 23 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.666666667 + -6x + x2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + -6x + -7.666666667 + x2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + -6x + x2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + -7.666666667 -6x + x2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 -6x + x2 = -7.666666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7.666666667 + 9 Reorder the terms: 9 + -6x + x2 = -7.666666667 + 9 Combine like terms: -7.666666667 + 9 = 1.333333333 9 + -6x + x2 = 1.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + -3) equal to 1.154700538 and -1.154700538.Subproblem 1
x + -3 = 1.154700538 Simplifying x + -3 = 1.154700538 Reorder the terms: -3 + x = 1.154700538 Solving -3 + x = 1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.154700538 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.154700538 + 3 x = 1.154700538 + 3 Combine like terms: 1.154700538 + 3 = 4.154700538 x = 4.154700538 Simplifying x = 4.154700538Subproblem 2
x + -3 = -1.154700538 Simplifying x + -3 = -1.154700538 Reorder the terms: -3 + x = -1.154700538 Solving -3 + x = -1.154700538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.154700538 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.154700538 + 3 x = -1.154700538 + 3 Combine like terms: -1.154700538 + 3 = 1.845299462 x = 1.845299462 Simplifying x = 1.845299462Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.154700538, 1.845299462}Solution
x = {4.154700538, 1.845299462}
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