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Simplifying 3x + 5 = 18x2 + -27x + -5 Reorder the terms: 5 + 3x = 18x2 + -27x + -5 Reorder the terms: 5 + 3x = -5 + -27x + 18x2 Solving 5 + 3x = -5 + -27x + 18x2 Solving for variable 'x'. Reorder the terms: 5 + 5 + 3x + 27x + -18x2 = -5 + -27x + 18x2 + 5 + 27x + -18x2 Combine like terms: 5 + 5 = 10 10 + 3x + 27x + -18x2 = -5 + -27x + 18x2 + 5 + 27x + -18x2 Combine like terms: 3x + 27x = 30x 10 + 30x + -18x2 = -5 + -27x + 18x2 + 5 + 27x + -18x2 Reorder the terms: 10 + 30x + -18x2 = -5 + 5 + -27x + 27x + 18x2 + -18x2 Combine like terms: -5 + 5 = 0 10 + 30x + -18x2 = 0 + -27x + 27x + 18x2 + -18x2 10 + 30x + -18x2 = -27x + 27x + 18x2 + -18x2 Combine like terms: -27x + 27x = 0 10 + 30x + -18x2 = 0 + 18x2 + -18x2 10 + 30x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 10 + 30x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 15x + -9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 15x + -9x2)' equal to zero and attempt to solve: Simplifying 5 + 15x + -9x2 = 0 Solving 5 + 15x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -1.666666667x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -1.666666667x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.5555555556 -1.666666667x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -1.666666667x + x2 = 0.5555555556 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 0.5555555556 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.5555555556 + 0.6944444447 Combine like terms: 0.5555555556 + 0.6944444447 = 1.2500000003 0.6944444447 + -1.666666667x + x2 = 1.2500000003 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.2500000003 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -0.8333333335 = 1.118033989 Simplifying x + -0.8333333335 = 1.118033989 Reorder the terms: -0.8333333335 + x = 1.118033989 Solving -0.8333333335 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.118033989 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.118033989 + 0.8333333335 x = 1.118033989 + 0.8333333335 Combine like terms: 1.118033989 + 0.8333333335 = 1.9513673225 x = 1.9513673225 Simplifying x = 1.9513673225Subproblem 2
x + -0.8333333335 = -1.118033989 Simplifying x + -0.8333333335 = -1.118033989 Reorder the terms: -0.8333333335 + x = -1.118033989 Solving -0.8333333335 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.118033989 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.118033989 + 0.8333333335 x = -1.118033989 + 0.8333333335 Combine like terms: -1.118033989 + 0.8333333335 = -0.2847006555 x = -0.2847006555 Simplifying x = -0.2847006555Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9513673225, -0.2847006555}Solution
x = {1.9513673225, -0.2847006555}
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