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Simplifying 6x2 + 16x + -18 = 0 Reorder the terms: -18 + 16x + 6x2 = 0 Solving -18 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 8x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + 8x + 3x2 = 0 Solving -9 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.666666667x + x2 = 0 + 3 2.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.666666667x + x2 = 3 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 3 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 3 + 1.777777780 Combine like terms: 3 + 1.777777780 = 4.77777778 1.777777780 + 2.666666667x + x2 = 4.77777778 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 4.77777778 Calculate the square root of the right side: 2.185812842 Break this problem into two subproblems by setting (x + 1.333333334) equal to 2.185812842 and -2.185812842.Subproblem 1
x + 1.333333334 = 2.185812842 Simplifying x + 1.333333334 = 2.185812842 Reorder the terms: 1.333333334 + x = 2.185812842 Solving 1.333333334 + x = 2.185812842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 2.185812842 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 2.185812842 + -1.333333334 x = 2.185812842 + -1.333333334 Combine like terms: 2.185812842 + -1.333333334 = 0.852479508 x = 0.852479508 Simplifying x = 0.852479508Subproblem 2
x + 1.333333334 = -2.185812842 Simplifying x + 1.333333334 = -2.185812842 Reorder the terms: 1.333333334 + x = -2.185812842 Solving 1.333333334 + x = -2.185812842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -2.185812842 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -2.185812842 + -1.333333334 x = -2.185812842 + -1.333333334 Combine like terms: -2.185812842 + -1.333333334 = -3.519146176 x = -3.519146176 Simplifying x = -3.519146176Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.852479508, -3.519146176}Solution
x = {0.852479508, -3.519146176}
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