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Simplifying 2x2 + -30x = 5x2 + -3x + -18 Reorder the terms: -30x + 2x2 = 5x2 + -3x + -18 Reorder the terms: -30x + 2x2 = -18 + -3x + 5x2 Solving -30x + 2x2 = -18 + -3x + 5x2 Solving for variable 'x'. Reorder the terms: 18 + -30x + 3x + 2x2 + -5x2 = -18 + -3x + 5x2 + 18 + 3x + -5x2 Combine like terms: -30x + 3x = -27x 18 + -27x + 2x2 + -5x2 = -18 + -3x + 5x2 + 18 + 3x + -5x2 Combine like terms: 2x2 + -5x2 = -3x2 18 + -27x + -3x2 = -18 + -3x + 5x2 + 18 + 3x + -5x2 Reorder the terms: 18 + -27x + -3x2 = -18 + 18 + -3x + 3x + 5x2 + -5x2 Combine like terms: -18 + 18 = 0 18 + -27x + -3x2 = 0 + -3x + 3x + 5x2 + -5x2 18 + -27x + -3x2 = -3x + 3x + 5x2 + -5x2 Combine like terms: -3x + 3x = 0 18 + -27x + -3x2 = 0 + 5x2 + -5x2 18 + -27x + -3x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 18 + -27x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(6 + -9x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -9x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -9x + -1x2 = 0 Solving 6 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 9x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 9x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 9x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 9x + x2 = 0 + 6 9x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 9x + x2 = 6 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 = 6 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + 9x + x2 = 26.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 4.5 = 5.123475383 Simplifying x + 4.5 = 5.123475383 Reorder the terms: 4.5 + x = 5.123475383 Solving 4.5 + x = 5.123475383 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 = 5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.123475383 + -4.5 x = 5.123475383 + -4.5 Combine like terms: 5.123475383 + -4.5 = 0.623475383 x = 0.623475383 Simplifying x = 0.623475383Subproblem 2
x + 4.5 = -5.123475383 Simplifying x + 4.5 = -5.123475383 Reorder the terms: 4.5 + x = -5.123475383 Solving 4.5 + x = -5.123475383 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 = -5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.123475383 + -4.5 x = -5.123475383 + -4.5 Combine like terms: -5.123475383 + -4.5 = -9.623475383 x = -9.623475383 Simplifying x = -9.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.623475383, -9.623475383}Solution
x = {0.623475383, -9.623475383}
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